Question

solve $3\frac{1}{2}x + 1 = 8$

Explanation:

Step1: Subtract 1 from both sides

First, we want to isolate the term with \( x \). So we subtract 1 from both sides of the equation \( 3\frac{1}{2}x + 1 = 8 \).

\( 3\frac{1}{2}x + 1 - 1 = 8 - 1 \)

Simplifying both sides, we get \( 3\frac{1}{2}x = 7 \).

Step2: Convert mixed number to improper fraction

The mixed number \( 3\frac{1}{2} \) can be converted to an improper fraction. To do this, we multiply the whole number part (3) by the denominator (2) and add the numerator (1), so \( 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2} \).

Now our equation becomes \( \frac{7}{2}x = 7 \).

Step3: Solve for \( x \)

To solve for \( x \), we multiply both sides of the equation by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \).

\( x = 7\times\frac{2}{7} \)

Simplifying the right - hand side, the 7 in the numerator and the 7 in the denominator cancel out, leaving \( x = 2 \).

Answer:

\( x = 2 \)