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```									    Today’s Lesson

Solving Multistep
Linear Inequalities
Unit 3-Lesson 10
Warm-Up Activity

Let’s warm up today by
practicing our algebra skills
with partners.
The sum of 3 and 40 percent of a
number is equal to 15.
What is the number?
Let x = a number   40% = 0.4
3 + 0.4x = 15     to “undo” a positive you
must use a negative
–3          –3
What you do to one side of
0.4 x = 12       the equation, be sure and do
to the other.
Let x = a number
3 + 0.4 x = 15
–3          –3
0.4 x = 12       to “undo”
multiplication you
0.4 0.4         must divide

What you do to one side
x = 30       of the equation, be sure
and do to the other.
The difference of 20 percent of a
number and 10 is equal to 90.
What is the number?
Let x = a number     20% = 0.2
0.2x –10 = 90    to “undo” subtraction you
+10 +10
What you do to one side
0.2 x = 100         of the equation, be sure
and do to the other.
Let x = a number

0.2x –10 = 90
+10 +10
0.2 x = 100    to “undo” multiplication
you must divide
0.2 0.2
What you do to one side
x = 500       of the equation, be sure
and do to the other.
Leo owns a small thrift shop where
the daily revenue averages \$650.

What can his costs be if he wants
a profit of at least \$525 per day?
Let x = costs
650 – x ≥ 525
–650      –650      to “undo” a positive you
must use a negative

–x ≥ –125   When you multiply or divide
both sides of an inequality by
–1     –1      a negative number, the
x ≤ 125      direction of the inequality
must be changed.

The costs must remain below \$125.
Whole-Class Skills Lesson

Today we will be solving
multistep linear equations.
• When solving one-step inequalities,
the steps are the same as the steps for
solving one-step equations.

• The only important difference is paying
inequality if you multiply or divide
both sides by a negative value.
• The same is true for multistep
inequalities.
Solve for x.
–3(2x – 4) + 2x – 5 < –13
–6x + 12 + 2x – 5 < –13 distribute the –3
–4x + 7 < –13     collect like terms
subtract 7 from
–7    –7       both sides
–4x < –20        divide by –4
–4    –4       reverse the
x>5         inequality
Solve for x.
4
x – 8 < 24
5
+8       +8       add 8 to both sides

5 4        5        multiply by the
     x < 32    
4 5        4         reciprocal

x < 40
        
Solve for x.
–3x + 1 ≥ 42   exponent first
–3x + 1 ≥ 16
subtract 1 from
–1 –1        both sides
–3x ≥ 15
–3 –3            divide by –3

reverse the
x ≤ –5      inequality
Solve for x.
4 + 5x – 6x < 32
exponent first
4 + 5x – 6x < 9
collect like terms
4–x<9
subtract 4 from
–4  –4
both sides
–x < 5
divide by –1
–1 –1
reverse the
x > –5        inequality
Solve for x.
3(4x + 5) ≤ 75
distribute the 3
12x + 15 ≤ 75
subtract 15
–15 –15        from both sides

12x ≤ 60     divide by 12
12 12

x≤5

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