Solving Absolute Value Equations Answers

A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?

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

What is the solution to –4|–2x + 6| = –24?

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

Which equation has no solution?

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?

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?

Which statement is true?

Which equation has no solution?

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?