Question

Can someone help me with this problem://

Answer 1

You can simply collect terms, subtract the constant and divide by the x-coefficient. It is generally considered easier to do those steps if you eliminate fractions first (multiply by 12).

Multiply by 12

... 4(x -1) +3(x +5) = 6

... 4x -4 +3x +15 = 6 . . . . . eliminate parentheses

... 7x +11 = 6 . . . . . . . . . . . .collect terms

... 7x = -5 . . . . . . . . . . . . . . subtract the constant 11

... x = -5/7 . . . . . . . . . . . . . divide by the x-coefficient

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Here it is the other way.

... x(1/3 +1/4) +(-1/3 +5/4) = 1/2

... (7/12)x + 11/12 = 1/2 . . add the fractions to finish collecting terms

... x + 11/7 = 6/7 . . . . . . . multiply by 12/7

... x = -5/7 . . . . . . . . . . . subtract 11/7

At the third step here, you could subtract 11/12 before doing the multiply. You get the same answer, but you have to do the extra conversion of 1/2=6/12.