Q13. - Algebra 1

Question

Solve each equation. Check your solution.

$6+3t=8t-14$

Step-by-Step Solution

Answer

The solution of the given equation is $t=4$.

Step 1. Write the given equation.

The given equation is “$6+3t=8t-14$”.

Step 2. Solve the given equation.

Solving,

$6+3t=8t-14$  (Given equation)

$6+3t-3t=8t-14-3t$  (Subtract $3t$ from both sides)

$6=5t-14$  (Simplify)

$6+14=5t-14+14$  (Add 14 to both sides)

$20=5t$  (Simplify)

$\frac{20}{5}=\frac{5t}{5}$  (Divide both sides by 5)

$4=t$  (Simplify)

$t=4$  (Write the variable on the left-hand side)

So, $t=4$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $t=4$ in the given equation $6+3t=8t-14$ to get,

$\begin{array}{l}6+3\left(4\right)=8\left(4\right)-14\\ 6+12=32-14\\ 18=18\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.