Question

Solve for v. 3|v+5|-11=-47 If there is more than one solution, separate them with commas.

Answer 1

Initially, the equation 3|v+5|-11=-47 suggests there are no solutions as an absolute value cannot be negative. However, if the equation contained a typo and should have been 3|v+5|-11= +47, the solutions would be v = 7, -17.

Step-by-step explanation:

To solve the equation 3|v+5|-11=-47 for v, follow these steps:

1. Add 11 to both sides of the equation: 3|v+5| = -36.
2. Divide both sides by 3: |v+5| = -12. Note that the absolute value equation can never be negative, so this means there are no solutions.

However, if there was a typographical error and the correct equation is 3|v+5|-11= -47, continue with these steps:

1. Add 11 to both sides of the equation: 3|v+5| = -36.
2. Divide both sides by 3: |v+5| = -12. Since the result of an absolute value cannot be negative, this step indicates a mistake in the original problem. Thus, we would need the correct equation to find a solution.

If the student meant to have +47 on the right side, not -47, continue with these steps:

1. Add 11 to both sides of the equation to get 3|v+5| = 36.
2. Divide both sides by 3 to get |v+5| = 12.
3. Now, split the absolute value equation into two separate equations: v+5 = 12 and v+5 = -12.
4. Solve for v in the first equation: v = 12 - 5 = 7.
5. Solve for v in the second equation: v = -12 - 5 = -17.

Thus, the two solutions are v = 7, -17.