Question $4 x-18=2 x+34$

Studdy Solution

STEP 1

1. The equation $4x - 18 = 2x + 34$ 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 addition, subtraction, and division will be used.

STEP 2

1. Simplify the equation by moving all terms involving $x$ to one side.
2. Move constant terms to the opposite side.
3. Solve for $x$ by isolating it.
4. Check the solution by substituting it back into the original equation.

STEP 3

Subtract $2x$ from both sides of the equation to move all $x$ -terms to one side:
$4x - 2x - 18 = 34$
Simplify:
$2x - 18 = 34$

STEP 4

Add 18 to both sides of the equation to move constant terms to the other side:
$2x - 18 + 18 = 34 + 18$
Simplify:
$2x = 52$

STEP 5

Divide both sides by 2 to solve for $x$ :
$\frac{2x}{2} = \frac{52}{2}$
Simplify:
$x = 26$

STEP 6

Check the solution by substituting $x = 26$ back into the original equation:
Original equation: $4x - 18 = 2x + 34$
Substitute $x = 26$ :
$4(26) - 18 = 2(26) + 34$
Calculate both sides:
$104 - 18 = 52 + 34$
$86 = 86$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{26}$

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