Inequality Word Problems

Setting up an equation can be helpful for solving word problems.

What if the word problem involves an inequality?

Solving inequality word problems is similar; however, instead of setting up an equation, set up an inequality.

Set up an inequality to represent the situation and solve for the unknown value.

The unknown value is the number of months Candice has had the puppy, which we will call *x*.

The amount of weight the puppy has gained each month is 4 pounds.

So, the weight he has gained since Candice got him is 4 pounds times the number of months she has had him, or 4*x*.

Then, as part of his current weight, add his original weight to 4*x*.

The puppy now weighs more than 30 pounds.

So, write the expression with an inequality sign, greater than 30, and solve.

4*x* + 10 | > | 30 |

4*x* + 10 - 10 | > | 30 - 10 |

4*x* | > | 20 |

4*x* ÷ 4 | > | 20 ÷ 4 |

*x* | > | 5 |

So, Candice has had the puppy for more than 5 months.

Sometimes solutions to inequalities are represented on a number line.

To use a number line representation, first, place an open circle on the tick mark at the maximum value (for less than) or minimum value (for greater than).

Then, extend an arrow from the circle to the left or right, depending on if the solutions are less than or greater than that value, respectively.

Draw a number line with an open circle on the 5 tick mark.

Then, draw an arrow extending to the right.