5

Solve and check each linear equation.$$3(x-2)+7=2(x+5)$$...

Question

Solve and check each linear equation.$$3(x-2)+7=2(x+5)$$

solve and check each linear equation. $$ 3(x-2)+7=2(x+5) $$



Answers

Solve each equation.
$$\frac{3 x-2}{7}=\frac{x+2}{5}$$

For Problem 57. I'm getting asked to solve the equation and check that my solution is correct. So I'm gonna go ahead and start by writing the equation to Fifth X plus 3/7 equals one minus 4/7 X and I want to begin by getting all my life terms together on the same side. So I'm thinking I'm gonna put my ex terms to the left and my constance to the right. Okay, so I'll do that by adding 4/7 X to both sides to keep the balance. Okay, 2/5 and 4/7. I can't add as they are, so I'm gonna go ahead and give them, like, denominators of 35. So 2/5 will become 14 35th and 4/7 and that's an X plus 4/7 over 35 would become 20 35th X. I still have the plus 3/7 equals one. So I'm gonna go ahead and to track the 3/7 and I'm gonna go ahead and add everything I have together. So I have 14 and 20 35th which is 34 35th x. This goes away equals 4/7. Since 4/7 and three sevens make a whole seventh on one. Okay, so in order to get the ex alone right now, it's multiplied by 34 35th. So I want to undo that by multiplying by the reciprocal. And I do this on both sides to keep the balance of the equation. The point of that is to get rid of all the new miracle values and leave X by itself. And then I'm gonna go ahead and multiply this after I simplify. So seven goes into seven. Once seven goes into 35 5 times two goes into four twice two goes and sorry, too. Goes into four twice and two goes into 34 17 times. So I'm looking at two times five, which is 10 over one time 17 which is 17. So this means X equals 10 17 before I officially declare that as the answer, I want to go ahead and check. So I'll do 2/5 times. 27th plus 3/7 is it equal to one? Minus 4/7. Times 27th. All right. Same simplification method here. So 4/17 plus three sevens equals one minus. Okay. Nothing to simplify here, so I just have 40 and seven times. Seven. Uh, any time you don't have a calculator, I want to remind you of the partial sums methods. So you would d'oh. Seven times 10 and then seven times seven and add them together. So seven times set tennis 70 and seven times seven is 49 I can easily add those together. And I get 119 in case I don't have a calculator handy. Okay, this is all gonna be great, but I'm gonna need some common denominators in orderto have this together. Uh, so common denominators. 7 17 I'm thinking the 1 19 is a multiple of seven and 17 which indeed it is because seven times 17 is 119. So all multiply this by seven over seven. And this by 17 over 17 and then I'm gonna turn one into 119 over 119 so I'll have 28 over 119 plus 17 times three is going to give me 51 over 119. Does that equal? 119 over 119 minus 40 over 119. Okay. 28 51 is 79 119th and then 119 minus 40 is take a guest. 79 119th. So this checks And that means this answer is indeed correct. 27th.

For this problem, we need to first open the brackets. And to do so, we used the distributive property. So upon opening the records, we have the next plus one calls for was still open. Inter bracket who are deployed by X minus three plus x on brackish closed. So this forgive me. Seven necks for plus seven would be equal to four multiplied by two X minus three. So this forgive me. So the next plus seven would be called toe eight X minus. Greta, it should be No sorry. No re subtract seven Exxon boats. Right. So, Dysart que me seven X minus seven X plus seven be Quito. Hey, Tex. Minor Feber necks minus 12. So this would give me X. My ass trails. Cool toe seven. Now I add 12 on both sides. So this give me X minus spread plus 12 for be Quito seven plus 12. So this would be X has 19. So now that I have the value affects, I can easily check the left cancer than the right and fade off. The original equation for elections would become seven multiplied by X plus one. So this would give me seven multiplied by 19 plus one. So seven multiplied by 20 Excuse me, 140 so are just similarly becomes four multiplied by X minus three minus x. So this gives me for multiplied by 19 minus three minus 19. So excuse me for multiplied by 19 minus off minus 16 which use me for multiplied by man Dean plus 16 which gives me four multiplied by 35 which is equal toe 100 40. And since relative record auditors except vehicle to 19.

So when we're solving an equation like the one given, our first step is to isolate the variable meaning we want to have variables on one side and constant on the other. In order to do this in this case, we need to add five. Remember, this is to both sides. When we do that, we will be left with seven X equals 77. Our next step is to find X, and we're gonna simply do that by undoing the operation. Give it so because seven is being multiplied by X, we're gonna divide both sides by seven. And that leaves us with X equal to 11. To check our solution, weaken Simply plug in this value for X. When we do that, we have seven times 11 minus five and that should give us 72. Well, 77 minus five equals 72 and 72 equals 72. So we are all set. X equals 11

So our first school with this problem will be to isolate the variable on one side. In order to do that, we can move the X from the right over till left by subtracting fax from both sides. When we do that will be left with just one x two x minus. X is just a one ax minus seven equals six. We then will further need to isolate in order to find X will add seven to both sides. When we do that, we find that X equals 13. Finally, to check our work, we can plug that in for the value of X and ensure that the two sides of our equation are equivalent. We do this. We have two times 13 minus seven equals six plus 13. Simplifying on the left. We find that 26 minus seven should equal six plus 13 which is 19 and in fact 26 minus seven is 19. We get 19 equals 19. So in fact, X equals 13 is our correct solution


Similar Solved Questions

5 answers
(Laplace Transforms) Find function whose Laplace transform is5 (s _ 2)
(Laplace Transforms) Find function whose Laplace transform is 5 (s _ 2)...
4 answers
A waiter believes that his daily tips from various customers have a slightly right skewed distribution with a mean of 10 euros and a standard deviation of 3 euros_ What is the probability that the average of 36 customers will be more than 14 euros?Select one: 0.88490.1151none of the othersalmost 1almost 0
A waiter believes that his daily tips from various customers have a slightly right skewed distribution with a mean of 10 euros and a standard deviation of 3 euros_ What is the probability that the average of 36 customers will be more than 14 euros? Select one: 0.8849 0.1151 none of the others almost...
5 answers
Figure below shows capacitorcapacitance7.72 HF; and resistor; with resistance R = 4.73 MQ; connectedseriesbattery, with € 25.0 The circuit has swritch; wnichinitially open_Whatcircuit'$ time constant (in seconds)?What the maximum charge (In pC) on the capacitor after the switch closed?What the current (in VA) through the resistor 10.0 after the switch dlosed?
figure below shows capacitor capacitance 7.72 HF; and resistor; with resistance R = 4.73 MQ; connected series battery, with € 25.0 The circuit has swritch; wnich initially open_ What circuit'$ time constant (in seconds)? What the maximum charge (In pC) on the capacitor after the switch cl...
5 answers
Cato_ lby Th2 moment Jeiahirg Fcho + Y-u tZt/ Ct) = € My-" @hb. nmen { Pxove 0} an aij
Cato_ lby Th2 moment Jeiahirg Fcho + Y-u tZt/ Ct) = € My-" @hb. nmen { Pxove 0} an aij...
5 answers
If be the estimator for the parameter p in a binomial distribution. For to have at least 100(1 _ a) % probability of being within a distance d of p, the sample size should be no smaller than 24/2 a) 4d2 28 2d2 0/2 2d2 None of the above
If be the estimator for the parameter p in a binomial distribution. For to have at least 100(1 _ a) % probability of being within a distance d of p, the sample size should be no smaller than 24/2 a) 4d2 28 2d2 0/2 2d2 None of the above...
5 answers
Question 5 (1 point) Consider the following 4x4 matrix411 M = ~43 2 -2 ~4 36Where a11=-2Find the determinant of M4Your Answer:Answer
Question 5 (1 point) Consider the following 4x4 matrix 411 M = ~4 3 2 -2 ~4 3 6 Where a11=-2 Find the determinant of M4 Your Answer: Answer...
5 answers
9 01 JUa31a.4OJ4U3313400JPUON01 Jua3JJAUOJ1u331J.!puousjnb 6e13409 + u 531435 341 ua4l zU[ -u"500 8 I0 wno PJxewzUS! wng [e!HJed u J504M Souas € 2q 40Pajamsue 12K1ON SL uogsano 137
9 01 JUa31a.4OJ 4U3313400J PUON 01 Jua3JJAUOJ 1u331J.!p uousjnb 6e13 40 9 + u 531435 341 ua4l zU [ -u "5 00 8 I0 wno PJxew zU S! wng [e!HJed u J504M Souas € 2q 40 Pajamsue 12K1ON SL uogsano 137...
5 answers
2Vx-4 (se logarithmic differentiaticn to find the derivative of y = (4 pts:) (x+5)8
2Vx-4 (se logarithmic differentiaticn to find the derivative of y = (4 pts:) (x+5)8...
4 answers
Due in 49 minutes. Due Fri 02/28/2020 11:59~14 25 and b 33 5964 and define T: R? 4 R? by T(x) 151Let MMxFind a preimage of b under T (1.2) Preview Are there other preimages? No_Points possible: Unlimited attempts. Score on last attempt: (0, 0.5). Score in gradebook: (0, 0.5) , Out of: (0.5, 0.5)LicenSubmit
Due in 49 minutes. Due Fri 02/28/2020 11:59 ~14 25 and b 33 59 64 and define T: R? 4 R? by T(x) 151 Let M Mx Find a preimage of b under T (1.2) Preview Are there other preimages? No_ Points possible: Unlimited attempts. Score on last attempt: (0, 0.5). Score in gradebook: (0, 0.5) , Out of: (0.5, 0....
1 answers
5i2p latoa ratonal Fcoulaton 6' collega Losoh {o-ycar [etitulion and theteo Kear (Aitutiona real altee4 [70 K1 Intrret 3di)cc Cmbnaten Cinier Jno Iut renon Vollzaiu D7 !FatioltHLletabend: 4 TD-nca DLIOAternuTuseerens IneitutionGijot-
5i2p latoa ratonal Fcoulaton 6' collega Losoh {o-ycar [etitulion and theteo Kear (Aitutiona real altee4 [70 K1 Intrret 3di)cc Cmbnaten Cinier Jno Iut renon Vollzaiu D7 !Fatiolt HLlet abend: 4 TD-nca DLIOA ternu Tuseerens Ineitution Gijot-...
5 answers
Por' Honb pwoda nnyerooo LEnaeACLnn 5at nomily dlcnibuind #t4 Mun0t 48.Zu k =d ruLandb' du Llllono UZ T Mlaineoahy Gertonkz randonknncon wnar Is {e Dcoabilty that ha &513 /a9 0 lemoerato Ibovo 99,6 F?Atopul #nio to dotol mriniitumn tumpteuuleFrulitcelrttarMfaollcnitie enl touid Inp wumpotatirteomanl onlyolneniy popuWic4er
por' Honb pwoda nnyerooo LEnaeACLnn 5at nomily dlcnibuind #t4 Mun0t 48.Zu k =d ruLandb' du Llllono UZ T Mlaineoahy Gertonkz randonknncon wnar Is {e Dcoabilty that ha &513 /a9 0 lemoerato Ibovo 99,6 F? Atopul #nio to dotol mriniitumn tumpteuule FrulitcelrttarMfaollcnitie enl touid Inp ...
5 answers
While working with an ideal gas, which pairs of variables are inversely proportional to each other (if all other factors remain constant)? 1.Pand n and T and Vand T A. 1and 2 only B. 2 only and 3 only D.1, 3, and 4 only E.3 and 4 only
While working with an ideal gas, which pairs of variables are inversely proportional to each other (if all other factors remain constant)? 1.Pand n and T and Vand T A. 1and 2 only B. 2 only and 3 only D.1, 3, and 4 only E.3 and 4 only...
1 answers
Show that if $\mathbf{r}(t)=f(t) \mathbf{i}+g(t) \mathbf{j}+h(t) \mathbf{k}$ is differentiable at $t=t_{0},$ then it is continuous at $t_{0}$ as well.
Show that if $\mathbf{r}(t)=f(t) \mathbf{i}+g(t) \mathbf{j}+h(t) \mathbf{k}$ is differentiable at $t=t_{0},$ then it is continuous at $t_{0}$ as well....
4 answers
In the diagram below, AMNO~APQR,MN X,MO =3,PQ =x+4, and PR = x Determine the length of MN [Only an algebraic solution can receive full credit ]
In the diagram below, AMNO~APQR,MN X,MO =3,PQ =x+4, and PR = x Determine the length of MN [Only an algebraic solution can receive full credit ]...
5 answers
Exercise 2. (Spts , Consider the curve5s2 (v3 3) = 7Use implicit differentiation to find(2a) (2.Spts)ds dv(2b) (2.Spts)dv ds
Exercise 2. (Spts , Consider the curve 5s2 (v3 3) = 7 Use implicit differentiation to find (2a) (2.Spts) ds dv (2b) (2.Spts) dv ds...
5 answers
G.8B26 In the tmangle DEF , DE 1 EF and EC 1 DF _Based on thc Information In thc diagram, what I$ thc approrimete Icngth 0 De70 121757793Fhn
G.8B 26 In the tmangle DEF , DE 1 EF and EC 1 DF _ Based on thc Information In thc diagram, what I$ thc approrimete Icngth 0 De7 0 121 757 793 Fhn...
5 answers
GnruTemenan() 2N0 ( N( + [email protected] 'NO (H 0, ( 2NO, (AHI" , ~[B0 H MHI , Vtlic cuthalpy of tlic teaction of tlic ICAction ahown bclow = N (} + 202 ( 2NO2( MI , 292Fn146292following
Gnru Temenan () 2N0 ( N( + [email protected] 'NO (H 0, ( 2NO, ( AHI" , ~[B0 H MHI , V tlic cuthalpy of tlic teaction of tlic ICAction ahown bclow = N (} + 202 ( 2NO2( MI , 292 Fn 146 292 following...
5 answers
20. Prove that AC and Beindependent if A and B are independent events
20. Prove that AC and Be independent if A and B are independent events...

-- 0.020727--