Final answer:
By applying the Distributive Property and the properties of equality to the given equation, and through combining like terms and simple arithmetic, we can prove step by step that x equals 2.
Step-by-step explanation:
Let's solve the equation step by step to prove that x = 2.
Given: 7 + 2x - 7x = -5(x - 3) - 2(6x - 8)
We start by applying the Distributive Property to eliminate the parentheses:
7 + 2x - 7x = (-5 × x + 15) - (12x - 16)
Now, let's distribute the negative sign in the second expression:
7 + 2x - 7x = (-5x + 15) - 12x + 16
Combine like terms on both sides:
-5x + 2x - 7x = -12x and 15 + 16 = 31, hence we have 7 + 2x - 7x = 31 - 5x - 12x
After combining like terms, we get:
7 - 5x = 31 - 17x
Add 17x to both sides to eliminate x from the right side:
7 - 5x + 17x = 31 - 17x + 17x
7 + 12x = 31
Now, subtract 7 from both sides:
7 + 12x - 7 = 31 - 7
12x = 24
Finally, divide both sides by 12 to find the value of x:
12x ÷ 12 = 24 ÷ 12
x = 2
Therefore, by applying properties of equality and the Distributive Property, we've proven that x equals 2.