We need to solve the following expression:
[tex]-7(x-2)=38-3x[/tex]The first step to solve this problem is to apply the distributive property on the left side of the equation. This is given by the sum of the products. We have:
[tex]\begin{gathered} -7x-2\cdot(-7)=38-3x \\ -7x+14=38-3x \end{gathered}[/tex]We need to change the terms that have "x" from the right to the left. To do that we need to add "3x" on both sides.
[tex]\begin{gathered} -7x+14+3x=38-3x+3x \\ -7x+3x+14=38 \\ -4x+14=38 \end{gathered}[/tex]Then we need to subtract "14" on both sides to isolate the term with x on the left. We have:
[tex]\begin{gathered} -4x+14-14=38-14 \\ -4x=24 \end{gathered}[/tex]Then we need to divide both sides by "-4".
[tex]\begin{gathered} \frac{-4x}{-4}=\frac{24}{-4} \\ x=-6 \end{gathered}[/tex]The value of "x" that solves this equation is -6.
