Question

Justify each step.

$15y+7=12-20y$

$35y+7=12$

$35y=5$

$y=\frac{1}{7}$

Short answer

$15y+7=12-20y$Given

$35y+7=12$Addition property of equality

$35y=5$Subtraction property of equality

$y=\frac{1}{7}$Division property of equality

Step-by-step solution

Step 1. Apply additional property of equality.

If $a=b$and $c=d$, then $a+c=b+d$.

Step 2. Description of step.

Add $20y$on each side of $15y+7=12-20y$and simplify.

$15y+7+20y=12-20y+20y$

$35y+7=12$

Step 3. Apply the subtraction property of equality.

If $a=b$and $c=d$, then $a-c=b-d$.

Step 4. Description of step.

Subtract 7 from each side of the equation obtained in step 2 to find the value of y.

$\begin{array}{c}35y+7-7=12-7\\ 35y=5\end{array}$

Step 5. Apply division property of equality.

If $a=b$and $c\ne 0$, then $\frac{a}{c}=\frac{b}{c}$.

Step 6. Description of step.

Divide each side of the equation obtained in step 4 by 35 to find the value of y.

$\begin{array}{c}\frac{35y}{35}=\frac{5}{35}\\ y=\frac{1}{7}\end{array}$

Therefore, the value of y is $\frac{1}{7}$.