Question

Tell whether the given value of the variable is a solution of the equation.

$\frac{y}{4} = -8; y =32$

Short answer

No, y = 32 is not the actual solution of the equation$\frac{y}{4} = -8$.

Step-by-step solution

Apply the concept of equation:

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement.

Example: 3x + 5 = 14 is an equation, in which 3x+5 and 14 are two expressions separated by an ‘’equal’’ sign.

What are the steps to solve an equation?

Step 1: Simplify each side of the equation by removing parenthesis and combining the like terms.

Step 2: Use addition or subtraction to isolate the variable term on one side (preferably in the left side).

Step 3: Use Multiplication or Division to solve for the variable.

Step 3: Tell whether the given value of the variable is a solution of the equation. y4  =  -8;  y  =  32

Solving the equation:

$\begin{array}{l}\frac{y}{4}=-8\\ 4·\frac{y}{4}=4·-8\left[\text{Multiplybothsidesby4}\right]\\ y=-32\end{array}$

No, the solution of the equation is not y = 32, the correct solution is y = – 32