6-3A Solving Multi-Step Inequalities Algebra 1 Glencoe McGraw-Hill Linda Stamper
6-3A Solving Multi-Step Inequalities
Algebra 1 Glencoe McGraw-Hill Linda Stamper
A multi-step inequality is solved by transforming the inequality more than one time. Undo addition or subtraction before undoing multiplication or division or you may make the problem more complicated to solve. Always remember the basic rule when isolating the variable:
Whatever you do to one side of the
inequality sign, you must also do to the
other side of the inequality sign.
>
Solve –9 – x < – 6.
Write the inequality. 6 x9
Undo the subtraction 9 93 x Undo the negative
variable, 1 1/
3 x
1reverse inequality symbol and simplify.
Solve.
5 3y2 1) 3 3
2y2 2 2
1y >
11 x21 2) 1 1
21 x2 2 2
/
6 x
3) Four times a number plus twelve is less than or equal to negative seven more than three.4) Two more than half a number is greater than twenty-seven.
Write an inequality and then solve.
3) Four times a number plus twelve is less than or equal to negative seven more than three.
4) Two more than half a number is greater than twenty-seven.
Write an inequality and then solve.
73 12n4
12 1216n4
4 4 4n
4 12n4
272n21
2 2
25n21 2 2
50n
Are your inequality signs in a
line?
Solve.
17
4 17x9x2)1
3x
174 17x7
21x7 7 7
+–+– 279 x5 x2 –x2
6x
x5
2745x3 45 45
2745
18x3 3 3
– 279 x5 x2)2
>/
>/
Solve.
>
5h5419 3)
55
h54 42
4
5
4
5
h30
/
30 h
>
83m12
487 4)
838
3
m124 8
4
4
12
4
12
m23
/
23 m
Solve.
<
922x34 5)
8928x12
84x12 12
8
12 7x
/
784x36 6)
247824x18
54x18 18
24
18 3x
Solve.
>
27.0y05.083.0 7)
10010027y5 38 2727
y5110 /
22 y
27.0y05.083.0
5 5 y22
<
9.0n6.01.2 8)
10109 n621
212112n6 / 2 n
9.0n6.01.2
6 6
Solve.
18x5312 10)
10x
9 95415x
15 1539x
1
6915x)9
6915x 18 18
x536
3
5
3
5
x10>/
82x54
45
45
102x 2 2
12x
21
82x54)11
Solve.
2x10312
310
310
2x40 2 2
x38
14
2x10312)12
38x
6-A3 Pages 311–313 #12–23,59–61.