Chapter 1.1, Problem 34E

To determine

To Solve: The equation, $-\frac{2}{5}y=4$

Answer to Problem 34E

  $y=-10$

Explanation of Solution

Given information:

The equation $-\frac{2}{5}y=4$

Concept and Formula Used:

Multiplication of numbers

Calculation:

The givem equation is

  $\begin{array}{l}-\frac{2}{5}y=4\\ \text{Multiply both sides by 5}\\ -\frac{2}{5}y\times 5=4\times 5\\ -2y=20\left(\text{Simplify}\right)\\ \text{Divide both sides by }\left(-2\right)\\ \frac{-2y}{-2}=\frac{20}{-2}\\ y=-10\left(\text{Simplify}\right)\end{array}$

To check put the value of $y=-10$ in the expression

  $\begin{array}{l}-\frac{2}{5}y=4\\ -\frac{2}{5}\left(-10\right)\stackrel{?}{=}4\\ -2\left(-2\right)\stackrel{?}{=}4\\ 4=4\\ \text{As LHS}=RHS\text{ therefore the solution is correct}\end{array}$

Conclusion:

Therefore, the solution the equation $-\frac{2}{5}y=4$ is $y=-10$