Splash Screen

Five-Minute Check (over Lesson 1–4)

CCSS

Then/Now

New Vocabulary

Key Concept: Addition / Subtraction Property of Inequality

Example 1:Solve an Inequality Using Addition or Subtraction

Key Concept: Multiplication / Division Property of Inequality

Example 2:Solve an Inequality Using Multiplication or Division

Example 3:Solve Multi-Step Inequalities

Example 4:Write and Solve an Inequality

Over Lesson 1–4

A. 5

B. 7

C. 11

D. 12

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

Over Lesson 1–4

A. 5

B. 7

C. 10

D. 20

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

Over Lesson 1–4

A. 5

B. 10

C. 20

D. 40

Evaluate the expression 5|xy – w| if w = –2, x = 1.5, and y = 4.

Over Lesson 1–4

A. {–41, 1}

B. {–41, –1}

C. {–1, 1}

D. {1, 2}

Solve the equation |b + 20| = 21.

Over Lesson 1–4

A. {7, 3}

B. {2, 3}

C. {–7, –3}

D. {–2, 3}

Solve the equation –4|a + 5| = –8.

Over Lesson 1–4

What is the solution to the equation2|3x – 1| – 1 = –5?

A.

B.

C.

D.

Content Standards

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Mathematical Practices

4 Model with mathematics.

You solved equations involving absolute values.

• 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.

4y – 3 < 5y + 2 Original inequality

4y – 3 – 4y < 5y + 2 – 4y Subtract 4y from each side.

–3 < y + 2 Simplify.

–3 – 2 < y + 2 – 2 Subtract 2 from each side.

–5 < y Simplify.

y > –5 Rewrite with y first.

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

Which graph represents the solution to 6x – 2 < 5x + 7?

A.

B.

C.

D.

Solve an Inequality Using Multiplication or Division

Solve 12 –0.3p. Graph the solution set on a number line.

Original inequality

Divide each side by –0.3, reversing the inequality symbol.

Simplify.

Rewrite with p first.

Solve an Inequality Using Multiplication or Division

Answer: The solution set is p | p –40.

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

What is the solution to –3x 21?

A. {x | x –7}

B. {x | x –7}

C. {x | x 7}

D. {x | x 7}

Solve Multi-Step Inequalities

Original inequality

Multiply each side by 2.

Add –x to each side.

Divide each side by –3, reversing the inequality symbol.

Solve Multi-Step Inequalities

A.

B.

C.

D.

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 ofpretzels & juice plus

the costof gasoline

is less thanor 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. up to 700 miles

B. up to 800 miles

C. more than 700 miles

D. more than 800 miles

RENTAL COSTS 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?