1-8A Number Systems Algebra 1 Glencoe McGraw-HillLinda Stamper Add closure property?
6-3B Solving Multi-Step Inequalities Algebra 1 Glencoe McGraw-HillLinda Stamper.
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Transcript of 6-3B Solving Multi-Step Inequalities Algebra 1 Glencoe McGraw-HillLinda Stamper.
6-3B 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:
Solving Multi–Step Inequalities
Whatever you do to one side of the
inequality sign, you must also do to the
other side of the inequality sign.
To solve inequalities that have variables on both sides of the inequality symbol, first collect the variable terms on one side.
Solve .
Write the problem.Collect variable terms on one side.
Undo addition and simplify.
Undo multiplication and simplify.
31x322x6 x6 x6
31x322 31 31
x39 3 3
x3
31x322x6
3x
To solve inequalities that have variables on both sides of the inequality symbol, first collect the variable terms on one side.
Solve .
Write the problem.Collect variable terms on one side.
Undo addition and simplify.
Undo multiplication and simplify.
31x322x6 x3 x3
3122x3
22 229x3
3 33x
31x322x6
</
When solving inequalities that contain grouping symbols, first use the distributive property.
Write problem. 2x3x33x6 Distribute and combine like terms.
6x3x318x6 6x318x9
Collect variable terms on one side.
x3x36 18x6
Isolate the variable using inverse operations.
18 1824x6
6 6 4x
.2x3x33x6Solve
Solve.
w6 w1264 w12w12w1864
81 81
w932
Leave the fraction
improper. It must be in lowest
terms.
Example 1 Example 255x219x6
x2 x25519x4
19 1936x4
4 49x
Example 315x9x216x5
x7 x715x216
15 15x21
2 2
x21
15x916x7
Use good form –
place the negative out front!
932
w
>/
21
x
If solving an inequality results in a statement that is always true, the solution is the set of all real numbers. If solving an inequality results in a statement that is never true, the solution is an empty set, written as .
Write problem.
Distribute and combine like terms.
Collect variable terms on one side.
x5x5
Result is a false statement.2728
.87x54x32x8Solve
Copy in your spiral notebook!
87x54x32x8
835x512x316x8 27x528x5
Write problem.
Distribute and combine like terms.
Collect variable terms on one side.
x2x2
Result is a true statement.
2424
.12x212x4x3Solve
Copy in your spiral notebook!
all real numbers
12x212x4x3 24x212x12x3 24x224x2
Write problem.
Distribute and combine like terms.
Collect variable terms on one side.
2424
Result is a true statement.
x2x2
.12x212x4x3Solve
all real numbers
12x212x4x3 24x212x12x3 24x224x2
Subtract 24 from each side.
Be sure to simplify the inequality to determine whether it is a true statement. If the inequality is true, the solution is the set of all real numbers. If the inequality is false, the solution is the empty set, written as .
xx
Solve.
2b323 1)
6 68 b9
9
98
b
29b6
>/
9
7m9 81m 2) m m
7m8 81 77
m8 88 8 8
m 11 11 m
</
54
x
10 10 810x 2 2
6210x 3x 3x
6x32x7
Solve.
6x5 x415x8 3)
x5 x56 15x7
151512 x7 7 7 3 x
6x5 15x12
2x327x 4)
Solve.
1x22x8x114x7 5)
x4 x4228
2x4x8x1128x7 2x428x4
Solve.
y4 y4
183
12y2y3y23y4 6)
12y6y3y23y4
18y43y4
all real numbers
7) One half of a number increased by one is greater than or equal to six less than one fourth of the number.
6n41
1n21
n41n
41
1 1
6n41
1n42
61n41
7n41
14
14
28n
Write an inequality and then solve.
8) Sixteen more than three fourths of a number is more than one eighth of the number less than 2.
n81
216n43
n81n
81
16 16
n81
216
216n87
14n87
78
78
16n
-2
Write an inequality and then solve.
n43
n86
6-A4 Pages 311–312 #26–33, 39–42, 44–47.