Algebra 1 Unit 2: Linear Inequalities

Solving and writing inequalities, compound inequalities and absolute value equations and inequalities. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Solving inequalitiesNo calculator

Solve $-3x+7>19$.

1. $x<-4$
2. $x>4$
3. $x>-4$
4. $x<4$

Question 2

Solving inequalitiesNo calculator

Solve $2(x-5)\le 4x+6$.

1. $x\ge 8$
2. $x\ge -8$
3. $x\le 8$
4. $x\le -8$

Question 3

Compound inequalitiesNo calculator

Solve $-5<2x+3\le 11$.

1. $-8<x\le 8$
2. $-4\le x<4$
3. $-1<x\le 7$
4. $-4<x\le 4$

Question 4

Solving inequalitiesNo calculator

Which value of $x$ is a solution of $4-x\ge 2x+10$?

1. $2$
2. $-3$
3. $-1$
4. $0$

Question 5

Inequalities from contextNo calculator

Maya has 40 dollars. She buys a ticket for 12 dollars and wants to spend the rest on snacks at 3.50 dollars each. What is the greatest number of snacks she can buy?

1. $7$
2. $9$
3. $8$
4. $11$

Question 6

Solving inequalitiesNo calculator

Solve $\frac{x}{-2}+1\ge 4$.

1. $x\le -6$
2. $x\le 6$
3. $x\ge -2$
4. $x\ge -6$

Question 7

Compound inequalitiesNo calculator

Solve $3x-1<-7$ or $2x+5>11$.

1. $x<-6 \text{ or } x>3$
2. $x<-2 \text{ or } x>3$
3. $x<-2 \text{ or } x>8$
4. $-2<x<3$

Question 8

Absolute valueNo calculator

Solve $|2x-3|=9$.

1. $x=6 \text{ or } x=3$
2. $x=6$
3. $x=6 \text{ or } x=-3$
4. $x=-6 \text{ or } x=3$

Question 9

Absolute valueNo calculator

Solve $|x+4|<6$.

1. $x<2$
2. $-10<x<2$
3. $-2<x<10$
4. $x<-10 \text{ or } x>2$

Question 10

Absolute valueNo calculator

Solve $|3x|-2\ge 7$.

1. $x\ge 3$
2. $x\le -3 \text{ or } x\ge 3$
3. $x\le -\frac{5}{3} \text{ or } x\ge \frac{5}{3}$
4. $-3\le x\le 3$

Question 11

Inequalities from contextNo calculator

A rental van costs 45 dollars plus 0.30 dollars per mile. You can spend at most 90 dollars. Which inequality describes the number of miles $m$ you can drive?

1. $45m+0.30\ge 90$
2. $45+0.30m\le 90$
3. $45+0.30m\ge 90$
4. $0.30+45m\le 90$

Question 12

Compound inequalitiesNo calculator

How many integers $x$ satisfy $-3\le 2x+1<9$?

1. $7$
2. $6$
3. $4$
4. $5$