Solve each equation. Check your solution. (Lesson 2 - 3)

$\frac{t}{8}-6=-12$

We can add or subtract the same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

We are given the equation $\frac{t}{8}-6=-12$, we add 6 to both sides of the equation as shown:

role="math" localid="1642667864363" $$\begin{gathered} \frac{t}{8}-6+6=-12+6 \\ \frac{t}{8}=-6 \end{gathered}$$

An equation is an expression containing two quantities separated by a = symbol.

Finding a solution to an equation involves separating the variable on one side of the equation and numbers on the other side.

We can multiply or divide by the same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

We have the equation $\frac{t}{8}=-6$, we multiply by 8 on both sides of the equation as shown:

$\begin{array}{l}\frac{t}{8}\times 8=-6\times 8\\ t=-48\end{array}$

Thus the solution of the given equation is$t=-48$

We substitute the value of the variable into the given equation:

$\begin{array}{l}\frac{t}{8}-6=-12\\ \frac{-48}{8}-6=-12\\ -6-6=-12\\ -12=-12\end{array}$

Since the above equation is satisfied, the solution $t=-48$is verified.