Question

Solve each equation. Check your solution.

$6+3t=8t-14$

Short answer

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

Step-by-step solution

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.