Question

Which equation has the same solution set as 4 - 2(x - 5) = x - 19?

a) 2(x + 5) = -8
b) 3(x – 3) = 9
c) x + 2 = 2x - 3
d) 3x - 4 = 2x + 7

Answer 1

The equation that has the same solution set as 4 - 2(x - 5) = x - 19 is b) 3(x - 3) = 9.

Step-by-step explanation:

To find which equation has the same solution set as 4 - 2(x - 5) = x - 19, we need to simplify and solve the given equation.

First, distribute the -2 to both terms inside the parentheses: 4 - 2x + 10 = x - 19.

Next, combine like terms: 14 - 2x = x - 19.

Transpose the x terms to one side and the constants to the other side: 14 + 19 = 3x.

Simplify: 33 = 3x.

Divide both sides by 3 to solve for x: x = 11.

Now, substitute the value of x into each of the answer choices and see which equation yields 11 as the solution:

a) 2(11 + 5) = -8 is false

b) 3(11 - 3) = 9 is true

c) 11 + 2 = 2(11) - 3 is false

d) 3(11) - 4 = 2(11) + 7 is false

Therefore, the equation that has the same solution set as 4 - 2(x - 5) = x - 19 is b) 3(x - 3) = 9.