Question $-(x+1)=3$

Studdy Solution

STEP 1

1. The equation $-(x+1) = 3$ is asking us to solve for $x$ .
2. This is a one-step equation with one solution.
3. The equation involves basic algebraic operations, specifically distribution and addition/subtraction.

STEP 2

1. Simplify the equation by removing the negative sign.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

To simplify the equation, distribute the negative sign across the terms inside the parentheses:
$-(x+1) = -x - 1$
This transforms the equation to:
$-x - 1 = 3$

STEP 4

To isolate $x$ , first add 1 to both sides of the equation:
$-x - 1 + 1 = 3 + 1$
This simplifies to:
$-x = 4$

STEP 5

Now, multiply both sides by $-1$ to solve for $x$ :
$x = -4$

STEP 6

Check the solution by substituting $x = -4$ back into the original equation:
Original equation: $-(x+1) = 3$
Substitute $x = -4$ :
$-((-4)+1) = 3$
Simplify the left-hand side:
$-(-3) = 3$

STEP 7

Simplify further:
$3 = 3$
Both sides are equal, confirming the solution is correct.
Therefore, the solution is:
$\boxed{-4}$

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