Solving Inequalities: math test, Grade 7 – download the PDF

1 Symbols and values / 4 pts

1. Write as an inequality: “\(n\) is at most 15.”
2. True or false: \(-7 \lt -9\).
3. Is 3 a solution of \(2x + 1 \ge 7\)?
4. Is \(-2\) a solution of \(4 - x \lt 5\)?

2 Solve and graph / 4 pts

Solve each inequality and graph its solution set on a number line.

1. \(4x - 5 \lt 15\)
2. \(-3x + 4 \ge 19\)

3 Negative coefficient with a fraction / 3 pts

Solve \(6 - \dfrac{x}{3} \le 2\) and state the solution set.

4 Gym membership / 4 pts

A gym charges a 20-dollar sign-up fee plus 18 dollars per month. Sam can spend at most 200 dollars. Let \(m\) be the number of months. Write an inequality, solve it, and interpret the answer.

5 Error analysis / 3 pts

Zoe solved \(-5x \lt 35\) and got \(x \lt -7\). Explain her mistake, give the correct solution, and check it with a value.

6 Whole-number solutions / 2 pts

List all whole numbers \(x\) that satisfy both \(3x + 1 \lt 17\) and \(x \ge 2\).