QuestionSolve of the variable: $x=$ $\square$ $3(2 x-5)-4 x=33$

Studdy Solution

STEP 1

1. The equation $3(2x - 5) - 4x = 33$ is a linear equation in one variable.
2. The goal is to find the value of $x$ that satisfies the equation.
3. Basic algebraic operations such as distribution, combining like terms, and solving linear equations will be used.

STEP 2

1. Expand the equation by distributing the multiplication.
2. Combine like terms.
3. Isolate the variable $x$ .
4. Solve for $x$ .
5. Verify the solution by substituting it back into the original equation.

STEP 3

Distribute the $3$ into the terms inside the parentheses:
$3(2x - 5) = 3 \cdot 2x - 3 \cdot 5$
This simplifies to:
$6x - 15$
The equation now becomes:
$6x - 15 - 4x = 33$

STEP 4

Combine like terms on the left side of the equation:
$6x - 4x - 15 = 33$
This simplifies to:
$2x - 15 = 33$

STEP 5

Add $15$ to both sides of the equation to isolate the term with $x$ :
$2x - 15 + 15 = 33 + 15$
This simplifies to:
$2x = 48$

STEP 6

Divide both sides by $2$ to solve for $x$ :
$\frac{2x}{2} = \frac{48}{2}$
This simplifies to:
$x = 24$

STEP 7

Verify the solution by substituting $x = 24$ back into the original equation:
Original equation:
$3(2x - 5) - 4x = 33$
Substitute $x = 24$ :
$3(2(24) - 5) - 4(24) = 33$
Calculate inside the parentheses:
$3(48 - 5) - 96 = 33$
Simplify further:
$3(43) - 96 = 33$
$129 - 96 = 33$
$33 = 33$
The left-hand side equals the right-hand side, confirming the solution is correct.
The solution is:
$x = 24$

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