Absolute Value In

Solve the equation then graph the solution set.

|x+3|=2

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William, Aiden, Mason, Avery, Benjamin, and Maya are in a math competition. They are given a real-life problem to solve: A company's profit (P) is given by the equation |4 - 3x| = 7, where x is the number of products sold. Can you help them find the possible values of x?

• x = 2, -5/3

• x = -1, 11/3

• x = 5, -7/3

• x = 0, 7/3

Answer explanation

The equation |4 - 3x| = 7 can be solved as 4 - 3x = 7 or 4 - 3x = -7. Solving these gives x = -1 and x = 11/3 respectively. Hence, the correct answer is x = -1, 11/3.

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x-50|=15

• |x+15|=50

• |50+x|=15

• No Solution

Tags

CCSS.HSA.CED.A.3

A golf ball manufacturer puts 390 golf balls in each box. The box can be off by 6 golf balls. Write an inequality that displays the acceptable amount of golf balls that can be in a box.

• |x - 6| < 390

• |x - 6| ≤ 390

• |x - 390| < 6

• |x - 390| ≤ 6

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh.  Any box that varies from the weight by more than 5g is sent back. What is an equation that shows the range of allowable weights for a box of crackers and what is the range?

• |w - 213| ≤ 5,         208 ≤ w ≤ 218

• |w - 213| ≤ 5,                   0 ≤ w ≤ 10

• |w - 5| ≤ 213,         208 ≤ w ≤ 218

• |w - 5| ≤ 213,                   0 ≤ w ≤ 10

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03

• |v-20|=0.03

• |v|-0.03=20

• |v-0.03|=20

Tags

CCSS.HSA.CED.A.3

Sam's house is 14 blocks from the school. Emily lives 6 blocks from Sam. Use an absolute value equation to determine Emily's distance for the school.

• |x + 6| = 10
  6, 14

• |x – 6| = 14
  20, 8

• |x – 14| = 6
  20, 8

• |x + 14| = 6
  6, 14

Tags

CCSS.HSA.CED.A.3

Aiden has a 2-meter long rope for a school project. He needs to cut it into pieces, each measuring 4x meters long. If the absolute difference between the original length of the rope and the total length of the cut pieces is 10 meters, what could be the value of x?

• x = 2, -3

• x = 4, -5

• x = 1, -4

• x = -2, 3

Answer explanation

The question asks for the value of x when a 2-meter rope is cut into pieces of 4x meters each, and the absolute difference between the original and total length of the pieces is 10 meters. The correct answer is x = -2, 3. This means that the pieces of rope are either 3 meters or -2 meters long, which when subtracted from the original length, gives a difference of 10 meters.

The rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Which inequality represents represents the acceptable number of words?

• |x - 30| < 500

• |x - 30| ≤ 500

• |x - 500| < 30

• |x - 500| ≤ 30

Which absolute value has these solutions?

• | x - 2 | = 6

• | x + 6 | = -2

• | x + 2 | = 6

• | x - 6 | = 2