9514 1404 393
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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<em>Check</em>
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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<em>Additional comment</em>
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 <em>positive</em> 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.
