Question

What is the value of x that makes the equation true?

Answer 1

To solve for the value of x that makes the equation true, we can start by simplifying the equation:
x - 3x = 2(4 + x)

Explanation:

Now, let's simplify each side of the equation step by step:

On the left side, combine like terms:

x - 3x is -2x, so the equation becomes:

-2x = 2(4 + x)

Now, distribute the 2 on the right side:

-2x = 8 + 2x

Next, let's get all the x terms on one side of the equation and the constants on the other side. To do that, we can add 2x to both sides of the equation:

-2x + 2x = 8 + 2x + 2x

This simplifies to:

0 = 8 + 4x

Now, subtract 8 from both sides to isolate the 4x term:

0 - 8 = 8 + 4x - 8

-8 = 4x

Finally, divide both sides by 4 to solve for x:

(-8) / 4 = (4x) / 4

-2 = x

So, the value of x that makes the equation true is x = -2.

Answer 2

`\begin{array}{lrcl}&x-3x&=&2(4+x)\\\\\textsf{Combine like terms:}& -\:\boxed{2}\:x&=&2(4+x)\\\\\textsf{Distribute:}&-\:\boxed{2}\:x&=&2\cdot \boxed{4}+2\cdot \boxed{x}\\\\\textsf{Simplify:}& -\:\boxed{2}\:x&=&\boxed{8}+\boxed{2}\:x\\\\\textsf{Combine like terms:}&-\:\boxed{2}\:x&&-\:\boxed{2}\:x}\\\\\cline{2-4}\\\textsf{Divide by coefficient:}&-4x&=&\boxed{8}\\\\&\frac{-4x}{\boxed{-4}}&=&\frac{\boxed{8}}{\boxed{-4}}\\\\\cline{2-4}\end{array}\\\\\\\phantom{wwwwwwwwwwww.......www}\boxed{x=-2}`

Explanation:

The given equation is:

`x-3x=2(4+x)`

Combine like terms on the left side of the equation:

`-2x=2(4+x)`

Distribute the 2 into the parentheses by multiplying it by both terms inside:

`-2x=2\cdot 4+2\cdot x`

Simplify:

`-2x=8+2x`

Subtract 2x from both sides of the equation:

`\begin{aligned}-2x-2x&=8+2x-2x\\\\-4x&=8\end{aligned}`

Divide both sides by the coefficient of -4:

`\begin{aligned}(-4x)/(-4)&=(8)/(-4)\\\\x&=-2\end{aligned}`

Therefore, the value of x that makes the equation true is x = -2.