Question(11) $3(x-4)-(3 x-4)=6 x$

Studdy Solution

STEP 1

1. The equation $3(x-4)-(3x-4)=6x$ is a linear equation in one variable.
2. The goal is to solve for the variable $x$ .
3. Basic algebraic operations such as distribution, combining like terms, and isolating the variable will be used.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Move all terms involving $x$ to one side of the equation.
3. Solve for $x$ by isolating the variable.
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $3$ across the terms in the parentheses:
$3(x-4) = 3x - 12$
Substitute back into the equation:
$3x - 12 - (3x - 4) = 6x$

STEP 4

Distribute the negative sign across the terms in the parentheses:
$-(3x - 4) = -3x + 4$
Substitute back into the equation:
$3x - 12 - 3x + 4 = 6x$

STEP 5

Combine like terms on the left side of the equation:
$(3x - 3x) + (-12 + 4) = 6x$
This simplifies to:
$-8 = 6x$

STEP 6

The equation is already simplified, so we can move directly to solving for $x$ .

STEP 7

Isolate $x$ by dividing both sides by 6:
$x = \frac{-8}{6}$
Simplify the fraction:
$x = -\frac{4}{3}$

STEP 8

Check the solution by substituting $x = -\frac{4}{3}$ back into the original equation:
$3\left(-\frac{4}{3} - 4\right) - \left(3\left(-\frac{4}{3}\right) - 4\right) = 6\left(-\frac{4}{3}\right)$
Simplify each term:
$3\left(-\frac{4}{3} - \frac{12}{3}\right) - \left(-4 - 4\right) = -8$
$3\left(-\frac{16}{3}\right) + 8 = -8$
$-16 + 8 = -8$
Both sides are equal, confirming the solution is correct.
The solution is:
$x = -\frac{4}{3}$

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