How to Get Rid of the Number Under x

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Earlier, you learned how to get rid of a number in front of $x$ . Now you’ll learn how to get rid of a number $x$ is divided by. It’s important to keep in mind that multiplication and division are inverse arithmetic operations. What multiplying can do, dividing can undo, and vice versa.

Rule

To Get Rid of a Number $x$ Is Divided By

When you have $x$ divided by a number, you have to multiply both sides of the equation by that exact number to get $x$ to stand alone.

When multiplying in equations, you have to multiply both sides of the equation with the same number. Here’s a recipe that will make it easy for you:

Rule

Recipe

1.: Change all the terms that are only numbers to one side. Remember to change sign.
2.: Change the terms that have an $x$ in them to the side you didn’t put the numbers on. Remember to change sign.
3.: Simplify the terms on each side.
4.: Multiply both sides by the number that $x$ is divided by.

Example 1

Solve $\frac{x}{2} + 3 = 5$ for $x$ .

\begin{array}{l} \frac{x}{2} + 3 & = 5 \\ \frac{x}{2} & = 5 - 3 \\ \frac{x}{2} & = 2 \\ 2 \cdot \frac{x}{2} & = 2 \cdot 2 \\ 2 \cdot \frac{x}{2} & = 2 \cdot 2 \\ x & = 4 \end{array}

Example 2

Solve $\frac{2 x}{3} + 2 = - \frac{2 x}{3} - 5$ for $x$ .

\begin{array}{l} \frac{2 x}{3} + 2 & = - \frac{2 x}{3} - 5 \\ \frac{2 x}{3} + \frac{2 x}{3} & = - 5 - 2 \\ \frac{2 x + 2 x}{3} & = - 7 \\ 3 \cdot \frac{4 x}{3} & = - 7 \cdot 3 \\ 3 \frac{4 x}{3} & = - 21 \\ 4 x & = - 21 \\ \frac{4 x}{4} & = - \frac{21}{4} \\ x & = - \frac{21}{4} \end{array}

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To Get Rid of a Number x Is Divided By

Recipe

To Get Rid of a Number $x$ Is Divided By