Solving Absolute Value Equations Answers…

Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct?

A

She is correct, because both solutions satisfy the equation.

B

She is not correct, because she made a sign error.

C

She is not correct, because there are no solutions.

D

She is not correct, because there is only one solution: x = 3.5.

2

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To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?

A

|x – 645| = 20; maximum guess: 635 beans

B

|x – 645| = 20; maximum guess: 665 beans

C

|x – 20| = 645; maximum guess: 635 beans

D

|x – 20| = 645; maximum guess: 665 beans

3

Which equation has no solution?

A

|4x – 2| = –6

B

|–2 – x| = 9

C

|3x + 6| = 6

D

|–2x + 8| = 0

4

Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?

A

496 meters and 500 meters

B

500 meters and 508 meters

C

492 meters and 508 meters

D

496 meters and 504 meters

5

Which number line represents the solutions to |–2x| = 4?

A

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 4 and one at 2.

B

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 4.

C

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 2.

D

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 8 and one at 8.

6

Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below.3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2

A

x=−6

B

x=−4

C

x=2

D

x=4

7

Which number line represents the solutions to |x + 4| = 2?

A

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 2.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 4.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 6.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 4 and one at negative 2.

8

Which number line represents the solutions to |x – 5| = 1?

A

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 4.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 4 and one at 6.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 5 and one at 1.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 1 and one at 5.

9

Which equation has only one solution?

A

|x – 5| = –1

B

|–6 – 2x| = 8

C

|5x + 10| = 10

D

|–6x + 3| = 0

10

Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?

A

|x – 112| = 0

B

|x – 112| = 4

C

|4 – 112| = x

D

|112 – 4| = x

11

Which number line represents the solutions to |x + 4| = 2?

A

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 2.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 4.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 6.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 4 and one at negative 2.

12

Which number line represents the solutions to |x – 5| = 1?

A

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 4.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 4 and one at 6.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 5 and one at 1.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 1 and one at 5.

13

For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid?

A

|323 – 50| = x

B

|323 + 50| = x

C

|x – 323| = 50

D

|x + 323| = 50

14

Which equation has no solution?

A

|–x – 3| = 5

B

|2x – 1| = 0

C

|5 – 3x| = –8

D

|–x + 9| = 0

15