Which equation has the same solution as 4 – 2(x – 5 ) = x – 19

Which equation has the same solution 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

The Correct Answer and Explanation is:

Let’s first solve the given equation:

4 – 2(x – 5) = x – 19

1. Distribute the -2 to both terms inside the parentheses: 4−2x+10=x−194 – 2x + 10 = x – 194−2x+10=x−19
2. Combine the constants on the left side: 14−2x=x−1914 – 2x = x – 1914−2x=x−19
3. Now, let’s move all terms involving xxx to one side and constants to the other side. First, add 2x2x2x to both sides: 14=3x−1914 = 3x – 1914=3x−19
4. Next, add 19 to both sides to move the constants: 33=3×33 = 3×33=3x
5. Finally, divide by 3 to solve for xxx: x=11x = 11x=11

So, the solution to the equation is x=11x = 11x=11.

Now, we will check which of the answer options has the same solution of x=11x = 11x=11.

Option A: 2(x + 5) = -8

1. Distribute the 2: 2x+10=−82x + 10 = -82x+10=−8
2. Subtract 10 from both sides: 2x=−182x = -182x=−18
3. Divide by 2: x=−9x = -9x=−9

This is not the same solution as x=11x = 11x=11.

Option B: 3(x – 3) = 9

1. Distribute the 3: 3x−9=93x – 9 = 93x−9=9
2. Add 9 to both sides: 3x=183x = 183x=18
3. Divide by 3: x=6x = 6x=6

This is not the same solution as x=11x = 11x=11.

Option C: x + 2 = 2x – 3

1. Subtract xxx from both sides: 2=x−32 = x – 32=x−3
2. Add 3 to both sides: 5=x5 = x5=x

This is not the same solution as x=11x = 11x=11.

Option D: 3x – 4 = 2x + 7

1. Subtract 2x2x2x from both sides: x−4=7x – 4 = 7x−4=7
2. Add 4 to both sides: x=11x = 11x=11

This is the same solution as x=11x = 11x=11.

Conclusion:

The correct answer is Option D: 3x – 4 = 2x + 7, as it has the same solution x=11x = 11x=11.