Question $-\frac{1}{2}=-\frac{5}{6}+\frac{1}{4} a$

Studdy Solution

STEP 1

1. We are solving for the variable $a$ in the equation.
2. The equation involves fractions, so we will need to perform operations with fractions.

STEP 2

1. Isolate the term involving $a$ .
2. Solve for $a$ by performing algebraic operations.

STEP 3

Start with the given equation:
$-\frac{1}{2} = -\frac{5}{6} + \frac{1}{4} a$
To isolate the term involving $a$ , add $\frac{5}{6}$ to both sides of the equation:
$-\frac{1}{2} + \frac{5}{6} = \frac{1}{4} a$

STEP 4

To solve for $a$ , first simplify the left side of the equation. Find a common denominator for the fractions $-\frac{1}{2}$ and $\frac{5}{6}$ .
The common denominator for 2 and 6 is 6. Convert $-\frac{1}{2}$ to a fraction with a denominator of 6:
$-\frac{1}{2} = -\frac{3}{6}$
Now, add the fractions:
$-\frac{3}{6} + \frac{5}{6} = \frac{2}{6} = \frac{1}{3}$
So, the equation becomes:
$\frac{1}{3} = \frac{1}{4} a$

STEP 5

To solve for $a$ , multiply both sides of the equation by 4 to eliminate the fraction on the right side:
$4 \times \frac{1}{3} = a$
$a = \frac{4}{3}$
The solution is $a = \boxed{\frac{4}{3}}$ .

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