Linear Inequalities Worksheets Page 17
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50Solving Multi-Step Inequalities
Solving Multi-Step Inequalities
Then
Now
Why?
You solved multi-
1
Solve linear
A salesperson may make a
step equations.
inequalities involving
base monthly salary and earn
(Lesson 2-3)
more than one
a commission on each of her
operation.
sales. To find the number of
sales she needs to make to pay
2
Solve linear
her monthly bills, you can use a
inequalities involving
multi-step inequality.
the Distributive
Property.
1
Solve Multi-Step Inequalities
Multi–step inequalities can be solved by
undoing the operations in the same way you would solve a multi-step equation.
Tennessee
Curriculum Standards
CLE 3102.3.4 Solve
Real-World Example 1
Solve a Multi-Step Inequality
problems involving linear
equations and linear
SALES
Write and solve an inequality to find the sales Mrs. Jones needs if she
inequalities.
earns a monthly salary of $2000 plus a 10% commission on her sales. Her goal is
3102.3.13 Solve multi-
step linear inequalities with
to make at least $4000 per month. What sales does she need to meet her goal?
one variable and graph the
base salary + (commission × sales) ≥ income needed
solution on a number line.
SPI 3102.3.5 Write and/or
2000 + 0.10x ≥ 4000
Substitution
solve linear equations,
0.10x ≥ 2000
Subtract 2000 from each side.
inequalities, and compound
inequalities including those
x ≥ 20,000
Divide each side by 0.10.
containing absolute value.
She must make at least $20,000 in sales to meet her monthly goal.
GuidedPractice
1.
FINANCIAL LITERACY
The Print Shop advertises a special to print 400 flyers
for less than the competition. The price includes a $3.50 set-up fee. If the
competition charges $35.50, what does the Print Shop charge for each flyer?
When multiplying or dividing by a negative number, the direction of the inequality
symbol changes. This holds true for multi-step inequalities.
Example 2
Inequality Involving a Negative Coefficient
Solve -11y - 13 > 42. Graph the solution on a number line.
-11y - 13 > 42
Original inequality
-11y > 55
Add 13 to each side and simplify.
-11y
_
_
55
<
Divide each side by -11, and reverse the inequality.
-11
-11
y < -5
Simplify.
The solution set is {y | y < -5}.
0
2
-10 -8 -6 -4 -2
GuidedPractice
Solve each inequality.
2A. 23 ≥ 10 - 2w
2B. 43 > -4y + 11
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Lesson 5-3
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