Linear Inequalities: math test, Grade 9 – download the PDF

1 Solving inequalities / 4 pts

Solve each inequality.

1. \(3x-7\le 11\)
2. \(-4x+5>21\)
3. \(2(x-3)\ge 5x+6\)

2 Compound inequalities / 3 pts

Solve each compound inequality and graph part (a).

1. \(-5\le 2x+3<9\)
2. \(3x<-9\) or \(x-4\ge 1\)

3 Absolute value equations / 4 pts

Solve each equation.

1. \(|x-6|=4\)
2. \(2|x+1|-5=7\)
3. \(|3x+2|=-1\)

4 Absolute value inequalities / 3 pts

Solve each inequality.

1. \(|x+2|\le 5\)
2. \(|2x-1|>9\)

5 Modeling / 4 pts

(a) A school club must raise at least $250 for a trip. It sells wristbands for $4 each, after paying $30 for the design. Write and solve an inequality for the number of wristbands \(w\). (b) A parcel must weigh 12 pounds, within 0.5 pound. Write and solve an absolute value inequality, then give the limits in kilograms (1 lb \(\approx\) 0.4536 kg), rounded to the hundredth.

6 True or false / 2 pts

Say whether each statement is true or false, and justify.

1. The inequality \(4x+1<4x+9\) has no solution.
2. From \(-3x\ge 12\) we get \(x\ge -4\).