NAME
5-6
DATE
Study Guide and Intervention
PERIOD
(continued)
Chapter 5
72
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Week
15,
Algebra
Graphing Inequalities in Two Variables
Solve Linear
Inequalities We can use a coordinate plane to solve inequalities with
one variable.
Example
Use a graph to solve 2x + 2 > -1.
Step 1 First graph the boundary, which is the related function.
Replace the inequality sign with an equals sign, and
get 0 on a side by itself.
y
2x
+
2
>
-1
Original inequality
Change < to = .
2x + 2 = -1
2x
+ 2 + 1 = -1 + 1
Add 1 to each side.
x
0
2x + 3 = 0
Simplify.
Graph 2x + 3 = y as a dashed line.
Step 2 Choose (0, 0) as a test point, substituting these values
into the original inequality give us 3 > -5.
Step 3 Because this statement is true, shade the half plane
containing the point (0, 0).
1
. Because the half-plane
Notice that
the x-intercept of the graph is at -1 −
2
1
to the right
.
of the x-intercept is shaded, the solution is x > -1 −
2
Exercises
Use a graph
to solve each inequality.
2. x - 2 > 2
3. -x + 1 < -3
1. x + 7
≤ 5
y
y
y
x
0
x
0
x
0
4. -x - 7 ≥ -6
5. 3x - 20 < -17
6. -2x + 11 ≥ 15
y
y
y
x
x
0
0
x
0
NAME
DATE
2-3
PERIOD
Study Guide and Intervention (continued)
Week
15,
Algebra
Solving Multi-Step Equations
Solve Multi-Step
Equations To solve equations with more than one operation, often
called multi-step
equations, undo operations by working backward. Reverse the usual
order of operations
as you work.
Example
Solve 5x + 3 = 23.
5x +
3 = 23
Original equation.
5x + 3 - 3 = 23 - 3
5x = 20
5x
20
−
=−
5
5
x=4
Subtract 3 from each side.
Simplify.
Divide each side by 5.
Simplify.
Exercises
Solve each equation. Check your solution.
2. 6x + 9 = 27
3. 5x + 16 = 51
4. 14n - 8 = 34
5. 0.6x - 1.5 = 1.8
7
6. −
p - 4 = 10
d - 12
7. 16 = −
3n
8. 8 + −
= 13
9. − + 3 = -13
14
4b + 8
-2
10. − = 10
7x - (-1)
-8
13. -4 = −
12
8
g
-5
11. 0.2x - 8 = -2
12. 3.2y - 1.8 = 3
k
14. 8 = -12 + −
15. 0 = 10y - 40
-4
Write an equation and solve each problem.
16. Find three consecutive integers whose sum is 96.
17. Find two consecutive odd integers whose sum is 176.
18. Find three consecutive integers whose sum is -93.
Chapter 2
22
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. 5x + 2 = 27