Question

Justify each step.

$x-2=\frac{2x+8}{5}$

$5\left(x-2\right)=2x+8$

$5x-10=2x+8$

$3x-10=8$

$3x=18$

$x=6$

Short answer

$x-2=\frac{2x+8}{5}$Given

$5\left(x-2\right)=2x+8$Multiplication property of equality

$5x-10=2x+8$distributive property

$3x-10=8$Subtraction property of equality

$3x=18$Addition property of equality

$x=6$Division property of equality

Step-by-step solution

Step 1. Apply the multiplication property of equality.

If $p=q$then, $rp=rq$.

Step 2. Description of step.

Multiply each side of the $x-2=\frac{2x+8}{5}$by 5 and simplify.

$\begin{array}{c}5\times \left(x-2\right)=5\times \frac{2x+8}{5}\\ 5\left(x-2\right)=2x+8\end{array}$

Step 3. Apply the distributive property.

Expand the left-hand side of the equation obtained in step 2 using the distributive property.

$5x-10=2x+8$

Step 4. Apply the subtraction property of equality.

If $p=q$and $r=s$, then $p-r=q-s$.

Step 5. Description of step.

Subtract $2x$ from each side of the equation obtained in step 3 to find the value of x.

$5x-10-2x=2x+8-2x$

$3x-10=8$

Step 6. Apply addition property of equality.

If $p=q$and $r=s$, then $p+r=q+s$.

Step 7. Description of step.

Add 10 on each side of $3x-10=8$and simplify.

$3x-10+10=8+10$

$3x=18$

Step 8. Apply the division property of equality.

Divide each side of the equation obtained in step 7 by 3 to find the value of x.

$\begin{array}{c}\frac{3x}{3}=\frac{18}{3}\\ x=6\end{array}$

Therefore, the value of x is 6.