Algebra 2 A Unit 2: Expressions, Equations, And Inequalities Lesson 5: Solving Inequalities

Solve the inequality. Graph the solution set. 26 + 6 b ≥ 2(3 b + 4)

All real numbers.

Objectives

Solve and graph inequalities. Write and solve compound inequalities.

Solve the inequality. -12>24x

x<-1/2

What inequality represents the sentence?The product of a number and 12 is no more than 15.

12n < 15

Solve the problem by writing an inequality. A club decides to sell T-shirts for $15 as a fundraiser. It costs $20 plus $9 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $150.

15x - (9x + 20) ≥ 150; x ≥ 28.33

Solve the compound inequality. Graph the solution. -2 ≤ 2 x - 4 < 4

1<x<4

Your math test scores are 68, 78, 90, and 91. What is the lowest score that you can earn on the next test and still achieve an average of at least 85?

98

Key Word

Compound Inequality

Is the inequality sometimes, always, or never true?-2(2x + 9) > -4x + 9

Never

Determine whether the inequality is always, sometimes, or never true. 4x-8>1+4(x+3)

Never is true.

Find the lesser of two consecutive integers with a sum greater than 16.

The LESSER number is Greater than or equal to 8. The LESSER number is Greater than or equal to 12. The LESSER number is Greater than or equal to 14.

5:6:7 ratio, 54cm.

The longest side is less than 21 cm.

Solve the inequality. 2(m-3)+7<21

m<10

Solve the inequality. 57-4t>13

t=11

Solve the inequality. -2(w+4)+9<-11

w>6

Solve the compound inequality. 9x<-27 and 4x>36

x<-3 or x>9

Solve the compound inequality. 2x>-10 and 9x<18

x>-5 or x<2