MHB How Do You Solve the Absolute Value Equation -3|x+5| + 1 = 7|x+5| + 8?

[mathdad]

-3|x+5| + 1 = 7|x+5| + 8 Solution:

-3|x+5| – 7|x+5| = 7
-10 |x+5| = 7
|x+5| = -7/10
x+5 = ±(-7/10)
x = ±(-7/10) – 5

x₁ = -7/10 – 5
x₁ = -57/10

x₂ = 7/10 – 5
x₂ = 2/10
x₂ = 1/5

Correct?

 

[MarkFL]

-3|x+5| + 1 = 7|x+5| + 8 Solution:

-3|x+5| – 7|x+5| = 7
-10 |x+5| = 7
|x+5| = -7/10

When you reach this point, then you should observe that you have a problem...can you identify the problem?

 

[mathdad]

When you reach this point, then you should observe that you have a problem...can you identify the problem?

The problem is |x+5| = -7/10. More clearly, the problem is the negative -7/10.

 

[mathdad]

No solution is the answer.