Linear Equation and Inequality in Two Variables

A twelve inch candle and an 18 inch candle are lit at 6pm. The 12 inch candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Identify the equation that models this situation.

• 12 - 0.5x = 18 - 2x

• 12 + 0.5x = 18 + 2x

• 12x - 0.5 = 18x - 2

• 12 - 6x = 18 - 2x 

-4x + 14 ≤ 54

• x ≥ - 10

• x ≤ -10

• x ≥ 10

• x ≤ 10

-3 < x + 6 ≤ 5

• -9< x  or   x≤ -1

• All Real numbers

• -9< x   and   x≤ -1

• -10< x   and   x≤ -7

Which is a solution of
5(v + 3) - 10v > -10

• v < 5

• v > 5

• v > -5

• v < -5

The school cafeteria seats 250 students. 203 students are already seated. Write and solve an inequality that represents the additional number of students that can be seated.

• 203 + s ≤ 250; 47 students

• 250 - 203 = x; 47 students

• 203 + s < 250; 47 students

• x + 203 = 250; 47 students

Your class needs to raise $1000 for a field trip. You have already raised $250. You all decide to sell coupon books. You earn $12.50 for each book sold.
Choose the inequality that represents the number of books you should sell to meet or exceed your goal.

• b(250 + 12.50) ≥ 1000

• 250 + 12.50b ≥ 1000

• 250 + 12.50 + b ≥ 1000

• b ≥ 1000 - 250 - 12.50

Find the Error
What error did the student make when solving the equation:
⅕x + 6 = ⅗x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

• The student found an incorrect common denominator

• The student did not multiply all terms by the common denominator

• The student did not use opposite operations appropriately

• The student did not correctly eliminate the variable from one side of the equation

²/₃(5x + 6) = 34

• 51

• 45

• 8

• 9

Which equation has x=9 as a solution

• 4 + x = 12

• 5x = 45

• 2x = 20

• x + 7 = 26

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5