# 4.09 Problem solving with inequalities

## Interactive practice questions

Construct and solve an inequality for the following situation:

"$5$5 groups of $p$p, added to $5$5, is less than $25$25."

Easy
Approx a minute

Construct and solve an inequality for the following situation:

"The sum of $2$2 groups of $x$x and $1$1 is at least $7$7."

Consider the following situation:

"$2$2 less than $4$4 groups of $p$p is no more than $18$18".

Sophia has a budget for school stationery of $\$32$$32, but has already spent \15.25$$15.25 on books and folders.

Let $p$p represent the amount that Sophia can spend on other stationery. Write an inequality that shows how much she can spend on other stationery, and solve for $p$p.

### Outcomes

#### NY-7.EE.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

#### NY-7.EE.4b

(b) Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q ≤ r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem.