Question $-12=2(2 x-1)-10$

Studdy Solution

STEP 1

1. The equation $-12 = 2(2x - 1) - 10$ is a linear equation.
2. We need to solve for the variable $x$ .
3. The equation involves basic algebraic operations, including distribution and combining like terms.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $2$ on the right side of the equation:
$-12 = 2 \cdot 2x - 2 \cdot 1 - 10$
Simplify the expression:
$-12 = 4x - 2 - 10$
Combine like terms on the right side:
$-12 = 4x - 12$

STEP 4

Add $12$ to both sides of the equation to begin isolating $x$ :
$-12 + 12 = 4x - 12 + 12$
Simplify both sides:
$0 = 4x$
Divide both sides by $4$ to solve for $x$ :
$\frac{0}{4} = \frac{4x}{4}$
Simplify:
$x = 0$

STEP 5

Check the solution by substituting $x = 0$ back into the original equation:
$-12 = 2(2(0) - 1) - 10$
Simplify inside the parentheses:
$-12 = 2(0 - 1) - 10$
$-12 = 2(-1) - 10$
Simplify further:
$-12 = -2 - 10$
Combine like terms:
$-12 = -12$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{0}$

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