Question

In the following exercises, determine whether the given values are solutions to the equation.

$6y+10=12y$

1. $y=\frac{5}{3}$
   
2. $y=-\frac{1}{2}$
   

Short answer

$y=\frac{5}{3}$is the solution for the equation$6y+10=12y$

Step-by-step solution

Step 1. Given information

The equation is $6y+10=12y$

Find value of y and choose correct option.

Step 2. Calculation

Combine like terms of the equation $6y+10=12y$

$$\begin{gathered} 6y-12y=-10 \\ -6y=-10 \end{gathered}$$

Divide by $-6$on both sides

$$\begin{gathered} y=\frac{10}{6} \\ y=\frac{5}{3} \end{gathered}$$

Correct option is a.$y=\frac{5}{3}$

Step 3. Explanation for wrong option

Substitute$y=-\frac{1}{2}$in equation$6y+10=12y$

$$\begin{gathered} 6\left(-\frac{1}{2}\right)+10=12\left(-\frac{1}{2}\right) \\ -3+10=-6 \\ 7\ne -6 \end{gathered}$$

so this is wrong option.