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Solve each equation.$-30=t+9 t$...

Question

Solve each equation.$-30=t+9 t$

Solve each equation. $-30=t+9 t$



Answers

Solve each equation. Check your answer. $$ -24=-10 t+3 $$

By this today, we're going to solve the equation minus two. T Cube is equal to 180 minus 30 t squared. We're going to start by dividing by two. So we get minus T Square. Does he could 54 t minus 15 t squared. They're going to take everything over to the right inside Onda. We can see that there's a factor of tea in every time so you can factor out this factor of t. So get t turns t squared minus 15 t plus 54. In order to fact this further, we're looking for the factory ization of this, uh, quadratic polynomial in order to, uh, factories this. We're looking for two numbers whose product is 54 whose some is minus 15. This tells us that we're looking for two negative numbers now, looking at the factory ization of 54 we have one in 54 two times 27 three times 18 six times nine. No, in fact, minus six minus nine is minus 15. I'm minus six times minus nine was 54. So this is our desired decomposition. So tee times T minus six times T minus nine on. This is equally Zahra. For this to equal zero, we need, um we need to set. Each of the three brackets equals zero and this will give us a solution. So the first bracket is just tea, and that's equal to zero. Solution is in then T minus six is equal to zero. Giving us tears of sex or T minus nine is equal to zero. Giving those tears equal to nine on hair are three solutions. Thank you.

Today we're going to solve the equation three times. T minus eight plus two. T is equal to seven plus t. First, we're going to expand this bracket and get three T minus 24 plus two. T is equal to seven plus t. Now we're going to combine the tease on the left hand side to get five. T minus 24 is equal to seven plus t. We're going to subtract T from both sides. Two sides to get 40 minus 24 is equal to seven and we're going to add 24 to both sides. Um, to get ah 31 and then we'll divide by four. To find t is equal to 31/4 on hair is a solution. Thank you.

Says the original problem here has variables and numbers on both sides. I need to add or subtract the variables and I need to add or subtract the numbers. I'm going to start by moving the variables. So I'm going to subtract 12 t from both sides. I need to do the same thing on both sides and going to line it up under the like term which was the 13. T 13 t minus 12. T Use me won t which is just t. I still have the plus nine. I bring down my equal sign 12 to minus 12. T is here. That's the whole reason I just decided to start with that because the original problem had a positive 12 t So I subtract 12 t That gives me zero, but I'm still left with nine on the right hand side. I need to isolate my tea. So to do that I will subtract Will do the opposite operation off Subtract nine on both sides On the left side, I get just t because these give me zero equals and the nine minus nine is zero. That is a number. My solution is zero. I checked this by substituting zero in everywhere. There's a t in the original problem in making sure I get a correct statement. So 13 time zero plus nine those that equal 12 times zero plus knife, 13 times 00 plus nine I'll keep finishing that side and I get nine on the other side. 12 times 00 plus nine Obviously, now I get the same thing on both sides, which means

So what we just need to solve for T in this equation. And to start off, we can just add five to both sides, and that's actually all you need to do. Three plus five gives you a and that's the final answer.


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