Framing and Solving Inequalities

Solving Inequalities

Multiple Choice

Evaluate the expression |4w + 3| if w = –2.

• 5

• 7

• 11

• 12

Multiple Choice

Evaluate the expression |2x + y| if x = 1.5 and y = 4.

• 5

• 7

• 10

• 20

Multiple Choice

Evaluate the expression 5|xy – w|

if w = –2, x = 1.5, and y = 4.

• 5

• 10

• 20

• 40

Multiple Choice

Solve the equation |b + 20| = 21.

• {–41, 1}

• {–41, –1}

• {–1, 1}

• {1, 2}

Multiple Choice

Solve the equation –4|a + 5| = –8.

• {7, 3}

• {2, 3}

• {-7, -3}

• {-2, 3}

Multiple Choice

What is the solution to the equation
2|3x – 1| – 1 = –5?

• x = $$-\frac{1}{3}$$

• x = 1

• x = $$-\frac{1}{3}$$ and x = 1

• no solution

You solved equations involving absolute
values. (Lesson 1–4)

• Solve one-step inequalities.

• Solve multi-step inequalities.

• set-builder notation

Solve an Inequality Using Addition or Subtraction

Solve 4y – 3 < 5y + 2. Graph the solution set on a number line.

Answer: Any real number greater than –5 is a solution

of this inequality.

A circle means that this
point is not included in
the solution set.

Solve an Inequality Using Addition or Subtraction

Multiple Choice

Which graph represents the solution to

6x – 2 < 5x + 7?

Solve an Inequality Using Multiplication or Division

Solve an Inequality Using Multiplication
or Division

A dot means that this
point is included in the
solution set.

Multiple Choice

What is the solution to –3x $$\ge$$ 21?

• {x | x ≥ –7}

• {x | x ≤ –7}

• {x | x ≤ 7}

• {x | x ≥ 7}

Solve an Inequality Using Multiplication or Division

Solve Multi-Step Inequalities

Multiple Choice

What is the solution to $$-2x\ >\ \frac{x\ +\ 5}{3}$$ ?

Write and Solve an Inequality

CONSUMER COSTS Javier has at most $15.00 to spend today. He buys a bag of pretzels and a bottle of juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Javier buy for his car?

Understand

Let g = the number of gallons of gasoline that Javier buys. The total cost of the gasoline is 2.89g. The cost of the pretzels and juice plus the total cost of the gasoline must be less than or equal to $15.00.

Write and Solve an Inequality

Original inequality

Subtract 1.59 from
each side.

Simplify.

The cost of

pretzels & juice

plus

the cost

of gasoline

is less than
or equal to

$15.00.

1.59

+

2.89g

15.00

Plan

Write an inequality.

Solve

Write and Solve an Inequality

Divide each side
by 2.89.

Simplify.

Answer: Javier can buy up to 4.6 gallons of gasoline

for his car.

Check

Since

is actually greater than 4.6,

Javier will have enough money if he gets no
more than 4.6 gallons of gasoline.

A. A
B. B
C. C
D. D

A

B

C

D

0%

0%

0%

0%

A. up to 700 miles

B. up to 800 miles

C. more than 700 miles

D. more than 800 miles

Multiple Choice

Jeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental?

• up to 700 miles

• up to 800 miles

• more than 700 miles

• more than 800 miles

​Questions?