Question $x+\frac{1}{2}=\frac{11}{12}$

Studdy Solution

STEP 1

1. The equation $x + \frac{1}{2} = \frac{11}{12}$ is asking us to solve for $x$ .
2. This is a one-step equation involving fractions.
3. The goal is to isolate $x$ by performing algebraic operations.

STEP 2

1. Understand the equation and the fractions involved.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

The equation $x + \frac{1}{2} = \frac{11}{12}$ involves adding a fraction to $x$ . We need to isolate $x$ .

STEP 4

To isolate $x$ , subtract $\frac{1}{2}$ from both sides of the equation:
$x + \frac{1}{2} - \frac{1}{2} = \frac{11}{12} - \frac{1}{2}$

STEP 5

Simplify the left side:
$x = \frac{11}{12} - \frac{1}{2}$
To subtract the fractions, find a common denominator. The least common denominator of 12 and 2 is 12.
Convert $\frac{1}{2}$ to $\frac{6}{12}$ :
$x = \frac{11}{12} - \frac{6}{12}$

STEP 6

Subtract the fractions:
$x = \frac{11 - 6}{12} = \frac{5}{12}$

STEP 7

Check the solution by substituting $x = \frac{5}{12}$ back into the original equation:
$\frac{5}{12} + \frac{1}{2} = \frac{11}{12}$
Convert $\frac{1}{2}$ to $\frac{6}{12}$ again:
$\frac{5}{12} + \frac{6}{12} = \frac{11}{12}$

STEP 8

Simplify the sum:
$\frac{11}{12} = \frac{11}{12}$
The left-hand side equals the right-hand side, confirming our solution is correct.
Therefore, the solution is:
$\boxed{\frac{5}{12}}$

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