Question

Find the value of k that makes the expressions below equivalent.

7+1/2x - 3 + 3/4x and 1 1/4x + k - 6

Answer 1

`7+\cfrac{1}{2}x-3+\cfrac{3}{4}x~~ = ~~\cfrac{5}{4}x+k-6\implies 7+\cfrac{x}{2}-3+\cfrac{3x}{4}~~ = ~~\cfrac{5x}{4}+k-6 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( 7+\cfrac{x}{2}-3+\cfrac{3x}{4} \right)~~ = ~~4\left( \cfrac{5x}{4}+k-6 \right)} \\\\\\ 28+2x-12+3x~~ = ~~5x+4k-24\implies 5x\boxed{-16}~~ = ~~5x+\boxed{4k-24} \\\\[-0.35em] ~\dotfill\\\\ -16~~ = ~~4k-24\implies 8=4k\implies \cfrac{8}{4}=k\implies {\Large \begin{array}{llll} 2=k \end{array}}`