holt ca course 1 11-8 solving two-step inequalities preview of grade 7 af4.1 solve two-step linear...
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Holt CA Course 1
11-8 Solving Two-Step Inequalities
Preview of Grade 7 AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
California Standards
Holt CA Course 1
11-8 Solving Two-Step Inequalities
When you solve two-step equations, you can use the order of operations in reverse to isolate the variable. You can use the same process when solving two-step inequalities.
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Draw a closed circle when the inequality includes the point and an open circle when it does not include the point.
Remember!
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
Additional Example 1A: Solving Two-Step Inequalities
y2 – 6 > 1
+ 6 + 6
y > 14
0 7 14 2171421– – –
Add 6 to both sides.
Multiply both sides by 2.
y2 – 6 > 1
y2 > 7
y2
> (2)7(2)
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Check
Additional Example 1A Continued
y 6 > 1 2
20 is greater than 14 Substitute 20 for y.
20 2
6 > 1 ?
4 > 1
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
Additional Example 1B: Solving Two-Step Inequalities
m –3
5 ≥ + 8
– 8 –8
m –33 ≥
m –3
5 ≥ + 8
m –3
(–3) ≤(–3) (–3)
m ≥ 9–3 0 3 6 9 12 15
•
Subtract 8 from both sides.
Multiply both sides by –3, andreverse the inequality symbol.
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution on a number line.
Additional Example 1C: Solving Two-Step Inequalities
4y – 5 < 11
4y – 5 < 11+ 5 + 5
4y < 16
4y < 164 4
y < 4
0 2 4 6–2–4–6º
Add 5 to both sides.
Divide both sides by 4.
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
Additional Example 1D: Solving Two-Step Inequalities
–4 ≥ –3x + 5
–4 ≥ –3x + 5
– 5 –5
–9 ≤ –3x
–3 –3
3 ≤ x
Subtract 5 from both sides.
Divide both sides by –3, and reverse the inequality symbol.
0 3 6 9–3–6–9
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
Check It Out! Example 1A
h7 + 1 > –1
– 1 – 1
h > –14
0 7 14 2171421– – –
Subtract 1 from both sides.
Multiply both sides by 7.
h7 + 1 > –1
h7 > –2
h7
> (7)(–2)(7)
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Check
Check It Out! Example 1A Continued
h + 1 > 1 7
7 is greater than 14 Substitute 7 for h.
7 7
+ 1 > 1 ?
2 > 1
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
m –2
+ 1 ≥ 7
– 1 –1 m–2
≥ 6
m –2
+ 1 ≥ 7
m –2 ≤ (6)(–2) (–2)
m ≤ –12–18 –12 –6 0 6 12 18
•
Subtract 1 from both sides.
Multiply both sides by –2, andreverse the inequality symbol.
Check It Out! Example 1B
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution on a number line.
2y – 4 > –12
2y – 4 > –12+ 4 + 4
2y > –8
2y > –82 2
y > –4
0 2 4 6–2–4–6º
Add 4 to both sides.
Divide both sides by 2.
Check It Out! Example 1C
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
–9x + 4 ≤ 31
–9x + 4 ≤ 31– 4 –4
–9x ≤ 27–9x ≥ 27–9 –9
x ≥ –3
Subtract 4 from both sides.
Divide both sides by –9, and reverse the inequality symbol.
0 3 6 9–3–6–9
Check It Out! Example 1D
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Sun-Li has $30 to spend at the carnival. Admission is $5, and each ride costs $2. What is the greatest number of rides she can ride?
Additional Example 2: Application
5 + 2r ≤ 30– 5 –5
2r ≤ 252r ≤ 252 2
Subtract 5 from both sides.
Divide both sides by 2.
r ≤ 12
252
, or 12
Sun-Li can ride only a whole number of rides, so the most she can ride is 12.
Let r represent the number of rides Sun-Li can ride.
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Brice has $30 to take his brother and his friends to the movies. If each ticket costs $4.00, and he must buy tickets for himself and his brother, what is the greatest number of friends he can invite?
Check It Out! Example 2
8 + 4t ≤ 30– 8 –8
4t ≤ 224t ≤ 224 4
Subtract 8 from both sides.
Divide both sides by 4.
t ≤ 5.5Brice can only buy a whole number of tickets, so the most people he can invite is 5.
Let t represent the number of tickets.