Writing Systems of Linear Inequalities Warmup

When you graph an inequality, you used a solid line when you use which symbols?

• ≤, ≥ 

• <, >

Answer explanation

You use a solid line when graphing inequalities with the symbols ≤ and ≥. This indicates that the values on the line are included in the solution set. In contrast, < and > use a dashed line, showing that the endpoints are not included.

Tags

CCSS.HSA.REI.D.12

When graphing an inequality, you use a dotted line when you use which symbol?

• <, >

• ≤, ≥ 

Answer explanation

You use a dotted line when graphing inequalities with the symbols < or >. This indicates that the points on the line are not included in the solution set, unlike ≤ or ≥, which use a solid line.

Tags

CCSS.HSA.REI.D.12

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system to represent the situation.

• x+y≤254
  5x+8y≥41

• x+41≤y
  5x+8y≥254

• x+y≤41
  5x+8y≥254

• x+y>41
  5x+8y<254

Answer explanation

The correct choice is x+y≤41 (total hours) and 5x+8y≥254 (minimum earnings). This represents the constraints of working hours and the required income to pay bills.

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

• x+y≤14
  2x+3y≤18

• 2x+3y≤14
  x+y≤18

• 2x+y<18
  x+3y<14

• x+14≤y
  2x+3y≤18

Answer explanation

The correct inequalities are x+y≤14 (tank capacity) and 2x+3y≤18 (budget constraint). This represents the maximum gallons and total cost of fuels x and y, respectively.

Select the correct graph for each inequality.

• A

• B

• C

• _D

Answer explanation

The correct graph for the inequality is B, as it accurately represents the solution set, showing the appropriate shading and boundary line for the given inequality.

Tags

CCSS.HSA.REI.D.12

Select the correct graph for each inequality.

• A

• B

• C

• D

Answer explanation

Graph A correctly represents the inequality by showing the appropriate shading and boundary line. The other options do not accurately reflect the given inequality.

Tags

CCSS.HSA.REI.D.12