Graphing Linear Inequalities and Word Problems

When graphing a linear inequality, < and > signs would require you to draw...

• a solid line

• a dotted line

• above the line

• below the line

Which of the following linear inequalities represents the graph?

Which of the following linear inequalities represents the graph?

Which inequality represents the graph?

• x ≤ -2

• x + 2y ≤ 6

• y ≤ -2x

• y < -2

Write the linear inequality in standard form for this situation: A landscaping business is purchasing plants from a nursery to finish a project. It will cost $14 each to buy each tree and $5 each to buy each bush. The landscaper wishes to keep the spending under $1000.

• 14x + 5y ≥ 1000

• 14x + 5y < 1000

• 14x + 5y  ≤ 1000

• 14x + 5y > 1000

Gideon needs to collect at least 1,000 signatures for a petition to free all Koalas from zoos. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which inequality represents this situation?

Aidan wants to spend under $15 on lunch. He decides to buy pizza slices, which cost $2.50 each and a two liter soda which costs $1.75. Which inequality represents this situation?

A limo driver needs to make more than $450 in one day.  He charges a rental fee of $375 and $0.85 per mile.  What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt, which inequality represents the highest possible price of the skirt?

• 20x + 120 ≥ 3

• x/3 + 20 ≤ 120

• 3x + 20 ≤ 120

• 3x + 20 ≥ 120