Page 520 - Algebra 1

L E S S O N Solving Two-Step and Multi-Step Inequalities 77
Warm Up
New Concepts
1. Vocabulary A(n) is a mathematical statement with two
(21)
equivalent expressions.
Solve and graph. 2.x-_1 >2
3.x+2.1<4.3 (66)
Solving Two-Step Inequalities
Solve each inequality and graph the solutions.
a. 8m-12≤-36 SOLUTION
8m - 12 ≤ -36
8m ≤ -24 Add 12 to both sides. m ≤ -3 Divide both sides by 8.
To graph the solutions, place a closed circle on -3 and shade the number line to the left of the closed circle.
(66) 3
4. _1 x ≤ -3
5. -5x ≥ 10 (70)
(70) 2
Two-step and multi-step inequalities require more than one inverse operation
to isolate the variable.
Example
1
Reading Math
< less than
≤ less than or equal to > greater than
≥ greaterthanorequalto
b. 9-3m>21
SOLUTION
9 - 3m > 21 -3m > 12
-6 -4 -2 0 2 4
Subtract 9 from both sides.
m < -4
To graph the solutions, place an open circle on -4 and shade the number
Divide both sides by -3 and reverse the direction of the inequality sign.
Math Reasoning
Write Why is an inequality graphed on a number line?
line to the left of the open circle.
-6 -4 -2 0 2 4
Before using inverse operations to isolate the variable, simplify each side of an inequality. Simplify by using the order of operations, distributing, combining like terms, or multiplying by the LCM of the denominators.
Lesson 77 505