Question

Place the statements and reasons in the correct order to solve the equation: -2(5a + 7) = -8a - 14

Answer 1

Sure, let's solve the given equation step by step:

-2(5a + 7) = -8a - 14

1. Distribute the -2 on the left side:

-10a - 14 = -8a - 14

2. Combine like terms by adding 8a to both sides:

-10a + 8a - 14 = -14

-2a - 14 = -14

3. Add 14 to both sides to isolate the term with 'a':

-2a = 0

4. Divide by -2 to solve for 'a':

a = 0

So, the solution to the equation is \( a = 0 \).

Answer 2

To solve the equation -2(5a + 7) = -8a - 14, distribute -2, eliminate parentheses, combine like terms, and solve for the variable a to get a = 0. Substituting the value back into the equation, the solution is verified.

Step-by-step explanation:

1. Distribute -2 to both terms in the parentheses: -10a - 14 = -8a - 14
2. Eliminate the parentheses by simplifying both sides of the equation: -10a - 14 = -8a - 14
3. Combine like terms on both sides of the equation: -10a + 8a = -14 + 14
4. Simplify the equation further: -2a = 0
5. Divide both sides of the equation by -2 to solve for a: a = 0
6. To check the answer, substitute a = 0 back into the original equation: -2(5(0) + 7) = -8(0) - 14
7. Simplify the equation: -2(7) = -14
8. Combine like terms: -14 = -14
9. The equation is balanced, and the solution is a = 0.