# Solving One-Step Linear Inequalities

Inequalities are mathematical sentences comparing two quantities that are not equal (or possibly not equal). There are five inequality symbols:

$x\ne 3$ | $x$ is not equal to $3$ |

$x<3$ | $x$ is less than $3$ |

$x>3$ | $x$ is greater than $3$ |

$x\le 3$ | $x$ is less than or equal to $3$ |

$x\ge 3$ | $x$ is greater than or equal to $3$ |

Some linear inequalities can be solved with a single operation. For this type of inequality, use the inverse operation to solve.

**
Example 1:
**

Solve for
*
$n$
.
*

$n+8<10$

The inverse operation of addition is subtraction. So, subtract $8$ from both sides.

$\begin{array}{l}n+8-8<10-8\\ n<2\end{array}$

**
Example 2:
**

Solve for $y$ .

$-3y\ge 15$

The inverse operation of multiplication is division. So, divide both sides by $-3$ .

IMPORTANT: Whenever you multiply or divide both sides of an inequality by a negative number, reverse the inequality.

$\begin{array}{l}\frac{-3y}{-3}\le \frac{15}{-3}\\ y\le -5\end{array}$

When you're done solving an inequality, you may be asked to graph it. See the lesson on Graphing Linear Inequalities if you need help.

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