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

AI Thread Summary
The absolute value equation -3|x+5| + 1 = 7|x+5| + 8 simplifies to -10|x+5| = 7, leading to |x+5| = -7/10. Since the absolute value cannot be negative, this indicates a fundamental issue with the equation. Therefore, the conclusion is that there are no solutions to the equation. The negative result confirms that the equation has no valid solutions. The final answer is no solution.
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-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?
 
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RTCNTC said:
-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?
 
MarkFL said:
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.
 
No solution is the answer.
 
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