Keystone Equations Inequalities

What is the solution set to the inequality: -3 < 2x - 1 < 7

• -2 < x < 4

• -1 < x < 3

• -1 < x < 4

• -1 < x < 4

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh.  Any box that varies from the weight by more than 5g is sent back. What is an equation that shows the range of allowable weights for a box of crackers and what is the range?

• |w - 213| ≤ 5,         208 ≤ w ≤ 218

• |w - 213| ≤ 5,                   0 ≤ w ≤ 10

• |w - 5| ≤ 213,         208 ≤ w ≤ 218

• |w - 5| ≤ 213,                   0 ≤ w ≤ 10

Which point below is NOT part of the solution set?

• (0, 0)

• (-10, 20)

• (3, 5)

• (0, -2)

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

A T-shirt company has a goal to earn a monthly profit of more than $3,500. The company charges $20 per T-shirt. The company has $1,500 in monthly costs. The inequality 20x - 1,500 > 3, 500 models this situation. Which BEST describes the meaning of x in the inequality?

• the profit made from the sale of 20 T-shirts

• the profit made from 1 month of T-shirt sales

• the number of T-shirts that need to be sold for the company to meet its goal

• the number of T-shirts that need to be sold for the company to recover its monthly costs

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000

• x+y<300
  7.5x+5.5y≥2000

• x+y≤300
  7.5x+5.5y≤2000

• x+y>2000
  7.5x+5.5y≤300

An inequality is shown below.

5x - 6 < 4 + 6x

Which is a graph of the solution set of the inequality?

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A part for a machine must meet certain length requirements, in centimeters (cm), as shown in the inequality below.

|6.75 - x| < 0.25

Which statement completely describes the length requirements for this machine part?

• The length of the part must be less than 7 cm.

• The length of the part must be greater than 6.5 cm.

• The length of the part must be less than 6.5 cm or greater than 7cm.

• The length of the part must be greater than 6.5cm and less than 7cm.

Which system of inequalities describes the graph?

• 4x + 3y > 24

  5x + 8y < 40

• 4x + 3y >= 24

  5x + 8y <= 40

• 4x + 3y < 24

  5x + 8y > 40

• 4x + 3y <= 24

  5x + 8y >= 40

Which values of a and b make the inequality true?

• a = 1, b = 1

• a = 1, b = 2

• a = 2, b = 0

• a = 2, b = 1