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PRE-ALGEBRA
Lesson 7-5 Warm-Up
PRE-ALGEBRA
“Solving Two-Step Inequalities”
(7-5)
Tip: Solve a multi-step inequality exactly like an equality (equaltion with an equal
How do you solve a
(3-1)
sign). Isolate the
variable (get the letter by itself) by:
multi-step inequality?
1. “Undo”ing addition and subtraction from the variable side
2. “Undo”ing multiplication and division from the variable side
Note: If the variables is on both sides, “undo” it from one side so that there is
only one variable side before doing anything else
PRE-ALGEBRA
Solving Two-Step Inequalities
LESSON 7-5
Additional Examples
Solve and graph 7g + 11 > 67.
7g + 11 > 67
7g + 11 – 11 > 67 – 11
Subtract 11 from each side.
7g > 56
Simplify.
7g
56
>
7
7
Divide each side by 7.
g>8
Simplify.
PRE-ALGEBRA
“Solving Two-Step Inequalities”
(7-5)
(3-1)
Example: Solve 2y – 3  -5.
2y - 3 + 3  -5 + 3
Add 3 to each side.
2y + 0  -2
Simplify.
2y
-2

2
2
y  -1
Check:
Divide each side by 2.
Simplify.
2y - 3  -5
2(-1) - 3
-5
Substitute -1 for y.
-5 = -5
2y - 3  -5
2(-2) - 3  -5
-7  -5
Check the direction of the inequality.
Substitute a solution less than – 1 for b like -2.
The direction of the sign is correct.
PRE-ALGEBRA
“Solving Two-Step Inequalities”
(7-5)
3-1)
1
Example: Solve -9  – x + 6.
3
-9  – 1 x + 6
3
-9 - 6  – 1 x + 6 - 6
3
-15  – 1 x + 0
3
3
3
1
– 1 (-15)  – 1 – 3 x
45  x or x  45
Add 6 to each side.
Simplify.
1
To eliminate the coefficient - 3 from the x side, divide both sides by
1
3
- 3 which is the same as multiplying each side by the reciprocal, - 1
When you divide or multiply both sides by a negative, reverse
the direction of the inequality symbol.
Simplify.
Check: -9  – 1 x + 6
3
1
-9  – (45) + 6
3
-9 = -9
-9  – 1 (60) + 6
3
-9  -14
Substitute 45 for x.
Check the direction of the inequality by substituting
x for a value bigger than 45, like 60.
The direction of the sign is correct.PRE-ALGEBRA
Solving Two-Step Inequalities
LESSON 7-5
Additional Examples
Solve 6 < – 2 r – 6.
3
6 < – 2r – 6
3
6+6 < – 2r–6+6
3
12 < – 2 r
3
Add 6 to each side.
Simplify.
3
3
2
– 2 (12) > – 2 – 3 r
Multiply each side by – 3 . Reverse the direction of
2
the inequality symbol.
–18 > r, or r < –18
Simplify.
PRE-ALGEBRA
Solving Two-Step Inequalities
LESSON 7-5
Additional Examples
Dale has $25 to spend at a carnival. If the admission
to the carnival is $4 and the rides cost $1.50 each, what is
the greatest number of rides Dale can go on?
Words
$4 admission +
Let r
Inequality
4
$1.50/ride
•
number
of rides
is less than
or equal to
$25
<
25
= number of rides Dale goes on.
+
1.5
•
r
PRE-ALGEBRA
Solving Two-Step Inequalities
LESSON 7-5
Additional Examples
(continued)
4 + 1.5r < 25
4 + 1.5r – 4 < 25 – 4
Subtract 4 from each side.
1.5r < 21
Simplify.
1.5r
21
<
1.5
1.5
Divide each side by 1.5.
r < 14
Simplify.
The greatest number of rides Dale can go on is 14.
PRE-ALGEBRA
Solving Two-Step Inequalities
LESSON 7-5
Lesson Quiz
Solve each inequality.
1. 14 > 4d – 10
d<6
3. 32 – 12g < 176
g > –12
2. –
k
+8 < 7
3
k>3
4. 8 + 5a > 23
a > 3
PRE-ALGEBRA