Linear Equations, Inequalities, and Systems

What is important to do when you divide or multiply by a negative when solving an inequality?

• The inequality sign must flip

• The inequality sign must stay the same

• Nothing happens

A system of equations with infinitely many solutions will have lines that...

• are the same

• cross in one place

• are parallel and never touch

A system of equations with no solution will have lines that...

• are the same

• cross in one place

• are parallel and never touch

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

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Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

• The first customer paid $12 for 14 postcards and 5 large envelopes.

• The second customer paid $24.80 for 10 postcards and 15 large envelopes.

What was the cost in dollars of each large envelope?

• $1.42

• $0.35

• $1.15

• $0.63

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Solve: |x + 3| < 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• 5 < x < 11

Solve:  |2x + 1| ≤ 19

• x ≥ 9 or x ≤ -10

• -10 ≤ x ≤ 9

• x ≥ 10 or x ≤ -9

• -9 ≤ x ≤ 10

What is the FIRST step to solving the equation:|x + 1| = 4

• Set up 2 equations

  x + 1 = 4

  x + 1 = -4

• Subtract 1 on both sides

• Set up 2 equations:

  x + 1 = 4

  x - 1 = 4

• Add 1 to both sides