Properties of inequality and properties of operations can be combined to solve inequalities using multiple steps.

As with equations, some inequalities require two or more steps to find the solution. Start by simplifying each side, if necessary. Apply the addition or subtraction property of inequality to isolate the term with the variable. Then apply the multiplication or division property to isolate the variable.

Step-By-Step Example

Solving Multistep Inequalities

Solve the inequality:

$4x-2 \lt 7+x$

Step 1

Apply the subtraction property of inequality to combine variable terms on one side of the inequality. Subtract $x$ from both sides.

$\begin{aligned} 4x-2&\lt 7+x\\4x-2-x&\lt 7+x-x\\3x-2&\lt 7\end{aligned}$

Step 2

Apply the addition property of inequality to undo the subtraction. Add 2 to both sides.

$\begin{aligned}3x-2&\lt 7\\3x-2+2&\lt 7+2\\3x&\lt 9\end{aligned}$

Solution

Apply the division property of inequality to undo the multiplication. Divide both sides by 3.

$\begin{aligned}3x&\lt 9\\\frac{3x}{3}&\lt \frac{9}{3}\\x&\lt 3\end{aligned}$