Question

$\frac{x + 3}{8} + \frac{x + 1}{3} = 3$

Explanation:

Step1: Find common denominator

The denominators are 8 and 3, so the common denominator is \( 8\times3 = 24 \). Multiply each term by 24 to eliminate fractions:
\( 24\times\frac{x + 3}{8}+24\times\frac{x + 1}{3}=24\times3 \)
Simplify each term:
\( 3(x + 3)+8(x + 1)=72 \)

Step2: Expand and combine like terms

Expand the parentheses:
\( 3x+9 + 8x+8 = 72 \)
Combine like terms:
\( (3x + 8x)+(9 + 8)=72 \)
\( 11x+17 = 72 \)

Step3: Solve for x

Subtract 17 from both sides:
\( 11x=72 - 17 \)
\( 11x=55 \)
Divide both sides by 11:
\( x=\frac{55}{11}=5 \)

Answer:

\( x = 5 \)