Question

Solve for x. 3(x-1)-8=4(1+x)+5 Also could someone please explain how to do this??

Answer 1

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Answer:

  x = -20

Step-by-step explanation:

First, simplify the equation. Eliminate parentheses and combine terms.

  3(x -1) -8 = 4(1 +x) +5 . . . . . . . given

  3x -3 -8 = 4 +4x +5 . . . . . . . . eliminate parentheses (distributive property)

  3x -11 = 4x +9 . . . . . . . . . . . . combine like terms

We can put all the x-terms on the right by subtracting 3x from both sides.

  3x -11 -3x = 4x +9 -3x

  -11 = x +9

And we can get the x-term by itself by subtracting 9 from both sides.

  -11 -9 = x +9 -9

  -20 = x . . . . . . . . . . this is the solution

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Check

3(-20 -1) -8 = 4(1 -20) +5

3(-21) -8 = 4(-19) +5

-63 -8 = -76 +5

-71 = -71 . . . . . . . . . true, the answer checks OK

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Additional comment

We observe that the two x-terms are 3x and 4x. The smaller of these is 3x, so when we subtract that from 4x we will have a positive result. That is why we chose to subtract 3x, even though it leaves the x-term on the right side of the equation. We could have subtracted 4x to get -x -11 = 9. I find it easier not to make a mistake if the variable has a positive coefficient.