Copy Flashback Friday 1-Linear Inequalities

Flashback Friday 1
Linear Inequalities

PAR.4.1 Create and solve linear inequalities in two variables to represent relationships between quantities including mathematically applicable situations: graph inequalities on coordinate axes with labels and scales

PAR.4.2 Represent constraints of linear inequalities and interpret data points as possible or not possible.

Multiple Select

When graphing $$y\ge-\frac{2}{7}x+1$$  , you will draw which of the following.

• A dotted line

• A solid line

• Shade up

• Shade down

Multiple Choice

Which of the following inequalities match the given graph?

• $$y\ge\frac{2}{5}x+1$$

• $$y\ge-\frac{2}{5}x+1$$

• $$y\le\frac{2}{5}x+1$$

• $$y\ge-\frac{2}{5}x-1$$

When solving inequality word problems, remember the key words and phrases that go along with each inequality symbol:

Multiple Choice

Vicky is studying French. She spends 1 hour reviewing each old chapter. She also spends 1.5 hours learning each new chapter. She spends at least 10 hours per week studying French.

Which graph could represent the possible number of old chapters Vicky reviews, x, and new chapters Vicky learns, y, each week?

Multiple Choice

A system of linear inequalities is shown.

Inequality 1: $$x\le5$$

Inequality 2: $$y>-2x+3$$

Which statement is true for the point (0,3)?

• The point (0,3) is a solution for inequality 2 but not for inequality 1.

• The point (0,3) is not a solution for this system of linear inequalities.

• The point (0,3) is the only solution for this system of linear inequalities.

• The point (0,3) is one of many solutions for this system of linear inqualities.

Multiple Choice

Is (0,0) a solution to the system?

• Solution
• Not a solution

Multiple Choice

Which of the following is not a solution to this system of inequalities?

• (0,-1)
• (0,3)
• (4,0)
• (6,-2)

​Word Problems

• Most of these problems will not be writing inequalities in slope-intercept form. (y = mx + b)

• You will be writing equations in standard form.

  (Ax + By > C) Rate(x) + Rate(y) > C

• Figure out what x and y represent

• Write an inequality for each topic &/or total

Multiple Choice

A computer store is placing an order for computers and tablets. Each computer costs $875, and each tablet costs $235. The store can spend at most $10,000 for these computers and tablets. The computer store has a limited amount of space for displaying the new computers and tablets. Each computer takes up 4 square feet of space, and each tablet takes up 3 square feet of space. The store has only 45 square feet of display space available for the new computers and tablets. The system of inequalities shown can be used to determine possible combinations of computers, x, and tablets, y, the store can order.

$$875x+235y\le10,000$$

$$4x+3y\le45$$

Which combination of computers, x, and tablets, y, can the computer store order?

• (8,4)

• (10, 2)

• (7, 9)

• (5, 9)

Multiple Choice

Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. If m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?

• 
  

  $$m+g\le40$$
  

  $$12m+14g\ge250$$
  

• $$m+g\ge40$$
  $$12m+14g\le250$$
  

• $$m+g\le40$$
  $$12m+14g\le250$$
  

• $$m+g\ge40$$
  $$12m+14g\ge250$$
  

Multiple Choice

Kim wants to earn at least $65 from her two jobs next week. At most, she can work 15 hours. Her first job (x) pays $5 per hour, and her second job (y) pays $7 per hour. Which system of inequalities describes Kim's situation?

• x + y > 15

  5x + 7y < 65

• $$x+y\le15$$
  $$5x+7y\ge65$$
  

• $$x+y\le65$$
  $$5x+7y\ge15$$
  

• x + y > 65

  5x + 7y < 15