Question

Solve each equation. Check your solution.

$14.2t-25.2=3.8t+26.8$

Short answer

The solution of the given equation is $t=5$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$14.2t-25.2=3.8t+26.8$”.

Step 2. Solve the given equation.

Solving,

$14.2t-25.2=3.8t+26.8$ (Given equation)

$14.2t-25.2-3.8t=3.8t+26.8-3.8t$ (Subtract $3.8t$from both sides)

$10.4t-25.2=26.8$ (Simplify)

$10.4t-25.2+25.2=26.8+25.2$ (Add $25.2$to both sides)

$10.4t=52$ (Simplify)

$\frac{10.4t}{10.4}=\frac{52}{10.4}$ (Divide both sides by $10.4$)

$t=5$ (Simplify)

So, $t=5$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $t=5$in the given equation $14.2t-25.2=3.8t+26.8$to get,

$\begin{array}{l}14.2\left(5\right)-25.2=3.8\left(5\right)+26.8\\ 71-25.2=19+26.8\\ 45.8=45.8\end{array}$

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.