Final answer:
To solve the algebraic equation -4(-6v+6)-v=7(v-4)-6, distribute the terms, combine like terms, and isolate the variable to simplify. After following the steps, the simplified form is v = -5/8, which should be checked for correctness.
Step-by-step explanation:
The equation -4(-6v+6)-v=7(v-4)-6 needs to be simplified to find the value of 'v'. Begin by distributing the multiplication over addition and subtraction: -4 * (-6v) + -4 * 6 - v = 7v - 7*4 - 6, which simplifies to 24v - 24 - v = 7v - 28 - 6.
Combine like terms to further simplify the equation: (24v - v) - 24 = 7v - 34. This simplifies to 23v - 24 = 7v - 34. Then, continue by subtracting 7v from both sides: 23v - 7v - 24 = -34. We get 16v - 24 = -34.
Next, add 24 to both sides to isolate the variable term: 16v - 24 + 24 = -34 + 24, or simply 16v = -10. Now divide by 16 to solve for 'v': v = -10/16, which can be reduced to v = -5/8.
Always check to ensure the solution is reasonable by substituting the value of 'v' back into the original equation and verifying both sides are equal.