How do you solve #-10abs(v+2)=-70#?

Question

Julia Adams · Accepted Answer

equating our two sides, #(v + 2)^2 = 7^2# 7^2 - #(v + 2)^2 = 0# #=> (v -2)(v + 2)(v + 7) = 0# #=> v = 5# => v + 2 - 7 = 0 # v = -9# since # v + 2 + 7 = 0

Julia Adams · Answer

undefined To solve the equation -10|v + 2| = -70, follow these steps:

1. Divide both sides by -10.
2. Rewrite the equation without absolute value.
3. Solve for v.
4. Check for extraneous solutions.

Solution:
1. |v + 2| = 7
2. v + 2 = 7 or v + 2 = -7
3. v = 5 or v = -9
4. Check both solutions in the original equation to ensure they are valid.

So, the solutions are v = 5 and v = -9.

Julia Adams · Answer

undefined To solve the equation -10|v + 2| = -70:

1. Divide both sides of the equation by -10 to isolate the absolute value expression: |v + 2| = 7.
2. Since the absolute value of a number is always positive, the expression inside the absolute value must either be equal to 7 or equal to -7.
3. Set up two separate equations based on these possibilities:
   a. v + 2 = 7
   b. v + 2 = -7
4. Solve each equation separately to find the possible values of v.
5. For equation (a): 
   v + 2 = 7
   Subtract 2 from both sides:
   v = 7 - 2
   v = 5
6. For equation (b):
   v + 2 = -7
   Subtract 2 from both sides:
   v = -7 - 2
   v = -9
7. Thus, the solutions to the equation are v = 5 and v = -9.