Practice Lesson 12 Compound Inequalities

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

Answer explanation

When graphing an inequality with ≤ or ≥, a closed dot is used to indicate that the endpoint is included in the solution set.

Tags

CCSS.6.EE.B.8

When graphing an inequality, you use an open dot when you use which symbol?

• <, >

• ≤, ≥ 

Answer explanation

When graphing an inequality, an open dot is used with the symbols < and > to indicate that the endpoint is not included in the solution set.

Tags

CCSS.6.EE.B.8

What inequality is graphed? 

• x > 2 and x ≤ -3

• x > 2 and x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

Answer explanation

The correct inequality graphed is x > 2 or x ≤ -3 because the graph shows a union of x values greater than 2 and x values less than or equal to -3.

Write an inequality for Graph 4.

• -2 < x < 5

• x < -2 or x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x ≤ 5

Answer explanation

The correct inequality for Graph 4 is -2 ≤ x ≤ 5, which represents all values of x from -2 to 5, including -2 and 5.

Solve: -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -2 ≤ x ≤ 6

• -3 ≤ x ≤ 3

• 1 ≤ x ≤ 3

Answer explanation

To solve the inequality, first add 1 to all parts: -3 + 1 ≤ 2x - 1 + 1 ≤ 5 + 1. This simplifies to -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3. Therefore, the correct answer is -1 ≤ x ≤ 3.

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5

• x < -5 and x > 5

• x < -5 or x > 5 

• x > -5 and x < 5 

Answer explanation

The correct answer is x < -5 or x > 5 because the inequalities x + 8 < 3 and -8x < -40 simplify to x < -5 and x > 5 respectively.

Solve:

3x + 2 < -7 or -4x + 5 < 1

• All real numbers

• x < -3 and x > 1

• x < -3 or x < 1

• x < -3 or x > 1

Answer explanation

The correct solution is x < -3 or x > 1. By solving the inequalities, we find that x can be any number less than -3 or greater than 1.

Mariah is solving the inequality -13<2x+5<15. Help Mariah find the solution set for x.

• -9>x>5

• -9<x<5

• -4<x<5

• -4>x>5

Answer explanation

The correct solution set is -9

What inequality is graphed on Kenzie's homework? 

• x > 2 and x ≤ -3

• x > 2 and x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

Answer explanation

The correct inequality graphed is x > 2 or x ≤ -3 because the graph shows values greater than 2 and values less than or equal to -3.

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