Question

solve for x. dont forget to perform a check.
\frac{4}{17}x = 24

x = \square

Explanation:

Step1: Isolate x by multiplying both sides by 17/4

To solve for \( x \) in the equation \( \frac{4}{17}x = 24 \), we multiply both sides by the reciprocal of \( \frac{4}{17} \), which is \( \frac{17}{4} \). This gives us:

$$ x = 24 \times \frac{17}{4} $$

Step2: Simplify the right-hand side

Simplify \( 24 \times \frac{17}{4} \). First, divide 24 by 4: \( 24 \div 4 = 6 \). Then multiply by 17: \( 6 \times 17 = 102 \). So \( x = 102 \).

Step3: Check the solution

Substitute \( x = 102 \) back into the original equation:

$$ \frac{4}{17} \times 102 = \frac{4 \times 102}{17} $$

Simplify \( 102 \div 17 = 6 \), then \( 4 \times 6 = 24 \), which matches the right-hand side of the original equation. So the solution is correct.

Answer:

\( x = 102 \)