Question $-(x-2)=3(2 x+3)$

Studdy Solution

STEP 1

1. The equation $-(x-2) = 3(2x+3)$ is asking us to solve for $x$ .
2. This is a linear equation involving distribution and simplification.
3. The equation can be solved using basic algebraic operations.

STEP 2

1. Simplify both sides of the equation.
2. Distribute and combine like terms.
3. Isolate the variable $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Start by simplifying both sides of the equation. On the left side, distribute the negative sign:
$-(x-2) = -x + 2$
On the right side, distribute the $3$ :
$3(2x+3) = 6x + 9$

STEP 4

Now, the equation is:
$-x + 2 = 6x + 9$
Combine like terms if necessary. In this case, there are no like terms to combine on either side.

STEP 5

To isolate $x$ , first move all terms involving $x$ to one side of the equation. Add $x$ to both sides:
$2 = 7x + 9$
Next, move the constant term to the other side by subtracting $9$ from both sides:
$2 - 9 = 7x$
$-7 = 7x$
Finally, divide both sides by $7$ to solve for $x$ :
$x = -1$

STEP 6

Check the solution by substituting $x = -1$ back into the original equation:
Original equation:
$-(x-2) = 3(2x+3)$
Substitute $x = -1$ :
$-((-1)-2) = 3(2(-1)+3)$
Simplify both sides:
Left side:
$-(-3) = 3$
Right side:
$3(-2+3) = 3(1) = 3$
Both sides are equal, confirming that the solution is correct.
The solution is:
$\boxed{-1}$

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