Question $4 x-11=11+2 x$

Studdy Solution

STEP 1

1. The equation $4x - 11 = 11 + 2x$ is a linear equation in one variable.
2. The goal is to find the value of $x$ that satisfies the equation.
3. We will use basic algebraic operations such as addition, subtraction, and division.

STEP 2

1. Simplify the equation by combining like terms.
2. Isolate the variable $x$ on one side of the equation.
3. Solve for $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Start by simplifying the equation. We want to get all terms involving $x$ on one side and constant terms on the other side.
Subtract $2x$ from both sides:
$4x - 2x - 11 = 11$

STEP 4

Simplify the left side by combining like terms:
$2x - 11 = 11$

STEP 5

Add 11 to both sides to isolate the term with $x$ :
$2x - 11 + 11 = 11 + 11$

STEP 6

Simplify both sides:
$2x = 22$

STEP 7

Divide both sides by 2 to solve for $x$ :
$\frac{2x}{2} = \frac{22}{2}$

STEP 8

Simplify the equation:
$x = 11$

STEP 9

Check the solution by substituting $x = 11$ back into the original equation:
Original equation: $4x - 11 = 11 + 2x$
Substitute $x = 11$ :
$4(11) - 11 = 11 + 2(11)$

STEP 10

Simplify both sides:
Left side: $44 - 11 = 33$
Right side: $11 + 22 = 33$
Since both sides are equal, the solution is verified.
The solution is:
$\boxed{11}$

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