Question

If ax - 7=b(x+2). then x =

Answer 1

$x=\frac{2b+7}{(a-b)}$

Explanation

$ax-7=b(x+2)$

Step 1

apply distributive property to eliminate the parenthesis

$\begin{gathered} ax-7=b(x+2) \\ ax-7=bx+2b \end{gathered}$

Step 2

add 7 in both sides

$\begin{gathered} ax-7=bx+2b \\ ax-7+7=bx+2b+7 \\ ax=bx+2b+7 \\ \end{gathered}$

Step 3

subtract bx in both sides

$\begin{gathered} ax=bx+2b+7 \\ ax-bx=bx+2b+7-bx \\ ax-bx=2b+7 \\ \text{factorize x} \\ x(a-b)=2b+7 \end{gathered}$

Step 4

finally, divide both sides by (a-b)

$\begin{gathered} \frac{x(a-b)}{(a-b)}=\frac{2b+7}{(a-b)} \\ \\ x=\frac{2b+7}{(a-b)} \end{gathered}$