Math Snap

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 $x$:
$$x = -1$$

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:
$$\boxed{-1}$$