# Two-Step Equations and Properties of Equality

## Key Questions

• To check solutions to two step equations, we put our solution back into the equation and check that both sides equal.

If they equal, then we know our solution is correct. If not, then our solution is wrong.

$x + 1 = \frac{1}{2} \left(2 x + 3\right)$

First step: Multiply both sides by 2:

$2 x + 2 = 2 x + 3$

Second step: Subtract $2 x$ from both sides:

$2 = 3$

• Solving two-step equations is not much more complicated than solving one-step equations; it just involves an extra step.

Usually there is more than one way to solve these. It's ok to use whatever method makes most sense to you. The general rule of thumb when isolating the variable is to undo the order of operations, PEMDAS. Start with addition and subtraction, then multiplication and division, then exponents, and finally parentheses.

Let's look at an example:$2 x - 6 = 12$

Method 1

$2 x - 6 = 12$
$2 x - 6 + 6 = 12 + 6$add 6 to each side
$2 x = 18$
$\frac{2 x}{2} = \frac{18}{2}$ divide each side by 2
$x = 9$

Method 2

$2 x - 6 = 12$
$\frac{2 x - 6}{2} = \frac{12}{2}$divide each side by 2
$\frac{2 x}{2} - \frac{6}{2} = \frac{12}{2}$ separate the fractions
$x - 3 = 6$ simplify
$x - 3 + 3 = 6 + 3$add 3 to each side
$x = 9$

• Step 1) Add or Subtract the necessary term from each side of the equation to isolate the term with the variable while keeping the equation balanced.

Step 2) Mulitply or Divide each side of the equation by the appropriate value solve for the variable while keeping the equation balanced.