Sure, let's solve the given equation [tex]\( \frac{5}{6} = \frac{x}{3} + \frac{1}{4} \)[/tex] step-by-step.
Step-by-Step Solution:
1. Find a common denominator to eliminate the fractions:
The denominators in the given equation are 6, 3, and 4. The least common multiple (LCM) of these denominators is 12.
2. Multiply every term by the common denominator (12):
[tex]\[
12 \cdot \frac{5}{6} = 12 \cdot \left( \frac{x}{3} + \frac{1}{4} \right)
\][/tex]
3. Simplify each term after multiplication:
[tex]\[
12 \cdot \frac{5}{6} = 12 \cdot \frac{5}{6} = 2 \cdot 5 = 10
\][/tex]
[tex]\[
12 \cdot \left( \frac{x}{3} \right) = 12 \cdot \frac{x}{3} = 4x
\][/tex]
[tex]\[
12 \cdot \left( \frac{1}{4} \right) = 12 \cdot \frac{1}{4} = 3
\][/tex]
4. Rewrite the equation with the simplified terms:
[tex]\[
10 = 4x + 3
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Subtract 3 from each side:
[tex]\[
10 - 3 = 4x + 3 - 3
\][/tex]
[tex]\[
7 = 4x
\][/tex]
Divide both sides by 4:
[tex]\[
\frac{7}{4} = x
\][/tex]
[tex]\[
x = \frac{7}{4}
\][/tex]
Therefore, the solution to the equation [tex]\( \frac{5}{6} = \frac{x}{3} + \frac{1}{4} \)[/tex] is [tex]\( x = \frac{7}{4} \)[/tex].
