Equations: cheat sheet

Algebra Foundations · The words and methods from the lessons, with an example of each.

A calculation with a letter in it. It has a value once you know the letter, but it does not say that anything is equal.

2x + 3

The value of the letter that makes the equation true.

x = 4

Each step has an opposite that undoes it: adding and subtracting, multiplying and dividing.

+ \leftrightarrow -\qquad \times \leftrightarrow \div

Undo the steps done to $x$ with their opposites, last step first.

\begin{aligned} 3x + 7 &= 19 \\ 19 - 7 &= 12 \\ 12 \div 3 &= 4 \end{aligned}

Take the same number of $x$ from both sides first, so the bags are on one side only.

\begin{aligned} 5x &= 2x + 12 \\ 3x &= 12 \\ x &= 4 \end{aligned}

Two expressions with = between them: a statement that they are equal, like a balanced scale.

2x + 3 = 11

Put the value in place of the letter and work out both sides. If they match, it is a solution. Check every answer in the first equation.

2(4) + 3 = 11 \checkmark

Do the same to both sides (take away, or share into equal groups) until $x$ is on its own.

\begin{aligned} 3x + 5 &= 20 \\ 3x &= 15 \\ x &= 5 \end{aligned}