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Solve equation and check your proposed solution. Begin your work by rewriting each equation without fractions.$ rac{z}{5}- rac{1}{2}= rac{z}{6}$...

Question

Solve equation and check your proposed solution. Begin your work by rewriting each equation without fractions.$ rac{z}{5}- rac{1}{2}= rac{z}{6}$

Solve equation and check your proposed solution. Begin your work by rewriting each equation without fractions. $\frac{z}{5}-\frac{1}{2}=\frac{z}{6}$



Answers

Solve equation and check your proposed solution. Begin your work by rewriting each equation without fractions. $\frac{z}{5}-\frac{1}{2}=\frac{z}{6}$

Okay, This question wants us to solve this equation. So to start, I'd like to get a common denominator on the left side because we have one fraction on the right. So it looks like both fractions need a two and a Z plus five. So our first fraction needs to pick up Z plus five, and then our second fraction needs to pick up a two, then writing what we have. We now have Z plus five times Z minus five over our common denominator vie nous three times to which is six over our common denominator. So then we can combine the fractions so our first fraction foils out toe Z squared plus Z minus C minus 25. Then we still have the negative six from the second fraction, and that's all divided by our common denominator. So now, combining like terms and simplifying our denominator, we get Z squared minus 31 over to Z plus 10 is equal to expanding the right side Z squared minus two Z minus three. And now we can see that these denominators could just clear out giving us Z squared minus 31 is equal to Ziese squared minus two z minus three. So Z squared is canceled. Leaving us with negative 31 is equal to negative two Z minus three or adding three to both sides. We get negative. 28 is equal to negative to see or Z is equal to 14.

Okay, here we have Z minus five. Z equals seven Z minus nine minus Izzy. Okay, combined. You're like terms. You could do both sides at the same time. Z minus five z. That's like one minus five. So negative four z over here. Seven Z minus Z. It's six z. So 60 minus nine. Then I want my letters to hang out on the same side. Also tracked six Izzy So negative Tensy. It was negative. Nine. And then divide both sides by negative. 10 two Negatives. Make a positive 9/10. You could do a decimal if you prefer. Check your answer by plugging it back in. We have one Z minus five Z. Supply me in 9/10. Then we have seven Z minus nine minus one more C minus 9/10. Okay, so 9/10 minus 45 10th. Seven times nine makes 63 10th. All right, so Ah, when we got nine minus 45 is negative. 36 times I combined. The 63 minus nine is 54. So 54 10th minus nine. Then we got to make a common denominator. So nine over one. If I multiply my 10 I get 90 over time and you can see 54. Minus 90. Makes negative 36. So the answer checks up. You can ease decibels and a calculator.

We'll start off by having four triple sites. These council out. We have negative five Z leftover and 21 plus four is 25. Then we'll divide both sides by negative five. Please cancel out and Z is equal to negative five.

To solve this. The first thing I'm going to do is distribute, so I'm going to distribute the negative five, which would give me negative five plus Tensy. Next, I'll distribute the four, which we give me, plus 12 minus for Z. Finally, I'll distribute the negative seven. Just be careful with that. Negative. Next, I'm going to combine all of my leg terms. I'm gonna put on my disease together to 10 minus for is six six. Minus seven gives me negative one z. Next, I will combine all of my like terms that don't have a variable to negative. Five plus 12 gives me seven seven. Minus 21 gives me a negative 14. So negative one Z minus 14 equals zero. I want my eyes, my variable variable to be positive. So I'm going to add one Z to both sides. So I'll get negative. 14 equals one z, which is you see, which is the same. A Z equals negative 14 to check. I would plug the negative 14 in frizzy and every place it shows up. So it tried those negative five times one negative two times negative. 14 B plus 28 plus four times three plus 14 minus seven times three minus 14 Checking does that equal zero The negative. Five times 29 plus four times 17 minus seven times negative. 11. Does that equal zero? So five times 29. So I would get negative 1 45 plus 68 plus 77. Does that equal zero? And that would give me zero equals zero, which means my


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