Question

Solve each equation. Check your solution.

$\frac{2}{5}b=-4$

Short answer

The solution of the equation is $b=-10$.

Step-by-step solution

Step-1. Apply the concept of multiplication and division of equality.

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

Finding 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 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 $\frac{2}{5}b=-4$, we divide $\frac{2}{5}$to both sides of the equation as shown:

$\frac{\frac{2}{5}b}{\frac{2}{5}}=\frac{-4}{\frac{2}{5}}$

Step-2. Simplify the expression.

Recall that:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times \frac{d}{c}$

Using this property of fractions we simplify the expression as shown:

$\begin{array}{l}\frac{\frac{2}{5}b}{\frac{2}{5}}=\frac{-4}{\frac{2}{5}}\\ \frac{2}{5}b\times \frac{5}{2}=-4\times \frac{5}{2}\\ b=-4\times \frac{5}{2}\end{array}$

Step-3. Write the solution.

$\begin{array}{l}b=-4\times \frac{5}{2}\\ b=-10\end{array}$

Thus, the solution of the equation is $b=-10$.

Step-4. Checking the solution.

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

$\begin{array}{l}\frac{2}{5}b=-4\\ \frac{2}{5}\times \left(-10\right)=-4\\ -4=-4\end{array}$

Since, the above equation is satisfied, the solution $b=-10$is verified.