Question

Solve each equation. Round to the nearest hundredth. Check your solution.

$5.4w+8.2=9.8w-2.8$

Short answer

The solution is$w=2.5$

Step-by-step solution

Step 1. Apply the concept of addition/subtraction and multiplication/division of equality.

We can add or subtract 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 can multiply or divide by 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.

Step 2. Solve the equation.

Using concepts mentioned in step $-1$, we solve equation as shown:

$\begin{array}{l}5.4w+8.2=9.8w-2.8\\ 5.4w-9.8w=-2.8-8.2\\ 5.4w-9.8w=-2.8-8.2\\ -4.4w=-11\\ w=\frac{-11}{-4.4}\\ w=2.5\end{array}$

Thus the solution of the given equation is $w=2.5$

Step 3. Checking the solution.

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

$\begin{array}{l}5.4w+8.2=9.8w-2.8\\ 5.4\left(2.5\right)+8.2=9.8\left(2.5\right)-2.8\\ 13.5+8.2=24.5-2.8\\ 21.7=21.7\end{array}$

Since, the above equation is satisfied, the solution $w=2.5$ is verified.