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How to Get Rid of the Number in Front of x

You have now learned how to move a term from one side of an equation to another. But what can you do when you are left with a number in front of $x$ ? You will learn what to do here.

It is important to remember that multiplication and division are inverse operations. What multiplication does, division can undo, and vice versa.

Rule

To Remove the Number in Front of $x$

When you have a number multiplied by $x$ , you need to divide both sides of the equation by that number to get $x$ on its own.

When you divide in an equation, you need to divide both sides of the equation by the same number. Here is a way to do it that will make it easy.

Rule

1.: Move all the terms that only consists of numbers to the right hand side. Remember to change $+$ to $-$ and $-$ to $+$ on the terms that move across the equal sign.
2.: Move all the terms with the unknown $x$ to the left side of the equation. Remember to change $+$ to $-$ and $-$ to $+$ on the terms you move across the equal sign.
3.: Simplify both sides.
4.: Divide both sides by the number in front of $x$ .

Example 1

Solve $2 x + 3 = 5$ for $x$ .

\begin{array}{l} 2 x + 3 & = 5 \\ 2 x & = 5 - 3 & (Item 1) \\ 2 x & = 2 & (Item 3) \\ \frac{2 x}{2} & = \frac{2}{2} & (Item 4) \\ \frac{2 x}{2} & = \frac{2}{2} \\ x & = 1 \end{array}

Example 2

Solve $3 x + 6 = 5 x + 12 + x$ for $x$ .

\begin{array}{l} 3 x + 6 & = 5 x + 12 + x \\ 3 x & = 5 x + x + 12 - 6 & (Item 1) \\ 3 x - 5 x - x & = 12 - 6 & (Item 2) \\ - 3 x & = 6 & (Item 3) \\ \frac{- 3 x}{- 3} & = \frac{6}{- 3} & (Item 4) \\ \frac{-3 x}{-3} & = \frac{6}{-3} \\ x & = - 2 \end{array}

How to Solve Equations (Change Sides, change sign)

How to Solve Linear Equations (Combined Methods)

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To Remove the Number in Front of x

To Remove the Number in Front of $x$