Page 521 - Algebra 1

Example
2
Solving Multi-Step Inequalities
Solve each inequality and graph the solutions.
Caution
Use the inequality symbol to determine if the circle is open or a closed.
≤ or ≥: closed circle
< or >: open circle
a. -8 + (-11) < -7d - 12
SOLUTION
-8 + (-11) < -7d - 12 -19 < -7d - 12
-7 < -7d 1 > d
Simplify the left side. Add 12 to both sides.
Divide both sides by -7 and reverse the direction of the inequality sign.
Place an open circle on 1. Shade the numbr line to the left of the circle.
b. -6(4 - x) ≥ -122 SOLUTION
-6(4 - x) ≥ -122
-24 + 6x ≥ -144 6x ≥ -120
-4 -2 0 2 4
Simplify both sides. Add 24 to both sides. Divide by 6.
Math Reasoning
Verify Show that the solution is the same
if both sides of the inequality are divided by –6.
x ≥ -20
Place a closed circle on -20. Shade the number line to the right of the circle.
c. _3y+_1<_7 4 2 10
SOLUTION
_3 y + _1 < _7 4 2 10
3(20) y+ 1(20) < 7(20) ___
5 10 2
-30 -20 -10
0 10 20 30
4 2 10 15y + 10 < 14
15y < 4 y < _4
15
Multiply by the LCM, 20.
Simplify.
Subtract 10 from both sides.
Divide both sides by 15.
Online Connection www.SaxonMathResources.com
Since _4 is a little less than _1 the distance between 0 and 1, estimate that 15 3 _4
distance on the number line. Place an open circle on 15 . Then shade the number line to the left of the open circle.
-1 0 1
506 Saxon Algebra 1