Question

Solve for x: -2(4 - 2x) + 3x = 2x + 2(5 + x) - 6 Options:

A) -4
B) -2
C) 2
D) 4

Answer 1

The equation -2(4 - 2x) + 3x = 2x + 2(5 + x) - 6 is solved by expanding and combining like terms on both sides, then isolating the variable x to find the solution. After simplifying the equation and solving for x, the correct answer is x = 4, which corresponds to Option D) 4.

Step-by-step explanation:

To solve the equation -2(4 - 2x) + 3x = 2x + 2(5 + x) - 6, let's first expand and simplify both sides:

Expand the left side: -2 * 4 + 2 * 2x + 3x = -8 + 4x + 3x

Combine like terms: -8 + 7x

Expand the right side: 2x + 2 * 5 + 2 * x - 6

Combine like terms: 2x + 10 + 2x - 6

Combine like terms: 4x + 4

Now, let's equate the two simplified sides:

-8 + 7x = 4x + 4

Next, subtract 4x from both sides to get:

-8 + 3x = 4

Add 8 to both sides:

3x = 12

Finally, divide both sides by 3 to solve for x:

x = 4

So the solution is x = 4, which means the correct answer is Option D) 4.