Interpret the Answer

Grace earns $7 for each car she washes. She always saves $25 of her weekly earnings. This week, she wants to have at least $65 in spending money. How many cars must she wash? Write and solve an inequality to represent this situation. Interpret the solution in context.

Critical Thinking

Is there any value of x with the property that x < x - 1? Explain your reasoning.

Analyze Relationships

A compound inequality consists of two simple equalities joined by the word “and” or “or.” Graph the solution sets of each of these compound inequalities.

a. \(\text{x} \gt 2\text{ and }\text{x} \lt 7\)

b. \(\text{x} \lt 2\text{ or }\text{x} \gt 7\)

c. Describe the solution set of the compound inequality \(\text{x} \lt 2\text{ and }\text{x} \gt 7\).

d. Describe the solution set of the compound inequality \(\text{x} \gt 2\text{ or }\text{x} \lt 7\).

Communicate Mathematical Ideas

Joseph used the problem-solving strategy Work Backward to solve the inequality \(2\text{n} + 5 \lt 13\). Shawnee solved the inequality using the algebraic method you used in this lesson. Compare the two methods.