Q. What is the value of \(x\) if \(\frac{2}{5}x – 17 = 15\)?

Add 17: \frac{2}{5}x = 32. Multiply by the reciprocal \frac{5}{2}: x = 32 \cdot \frac{5}{2} = 80.

Add 17 to both sides to get \frac{2}{5}x = 32, then multiply both sides by \frac{5}{2} (the reciprocal of \frac{2}{5}) to get x = 80.

\frac{5}{2} is the multiplicative inverse of \frac{2}{5}. Multiplying removes the coefficient: \frac{5}{2} \cdot \frac{2}{5}x = x.

Substitute x = 80: \frac{2}{5} \cdot 80 - 17 = 32 - 17 = 15, which matches the right side, so x = 80 is correct.

Then \frac{2}{5x} = 32, so 5x = \frac{2}{32} = \frac{1}{16}, giving x = \frac{1}{80}.

Answer

Add 17:
\[
\frac{2}{5}x=32
\]
Multiply by 5/2:
\[
x=32\cdot\frac{5}{2}=80
\]

Write the original equation exactly as given:

\[\frac{2}{5}x – 17 = 15\]

Explanation: The goal is to isolate the variable x. Start by undoing operations that are applied to x in reverse order.
Undo the subtraction of 17 by adding 17 to both sides to keep the equality balanced:

\[\frac{2}{5}x – 17 + 17 = 15 + 17\]

Simplify both sides:

\[\frac{2}{5}x = 32\]

Explanation: Adding 17 cancels the -17 on the left, leaving only the term with x. The right-hand side becomes 32.
Isolate x by removing the coefficient \(\frac{2}{5}\). Multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\):

\[x = 32 \cdot \frac{5}{2}\]

Compute the product step by step:

\[32 \cdot \frac{5}{2} = (32 \div 2) \cdot 5 = 16 \cdot 5 = 80\]

Explanation: Multiplying by the reciprocal cancels the fraction coefficient, leaving x alone.
Check the solution by substituting \(x = 80\) back into the original equation:

\[\frac{2}{5}\cdot 80 – 17 = 32 – 17 = 15\]

Explanation: The left-hand side equals the right-hand side, so the solution is correct.
\[x = 80\]

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Homework Answers

Add 17: \(\frac{2}{5}x = 32\). Multiply by the reciprocal \(\frac{5}{2}\): \(x = 32 \cdot \frac{5}{2} = 80\).

Add 17 to both sides to get \(\frac{2}{5}x = 32\), then multiply both sides by \(\frac{5}{2}\) (the reciprocal of \(\frac{2}{5}\)) to get \(x = 80\).

\(\frac{5}{2}\) is the multiplicative inverse of \(\frac{2}{5}\). Multiplying removes the coefficient: \(\frac{5}{2} \cdot \frac{2}{5}x = x\).

Substitute \(x = 80\): \(\frac{2}{5} \cdot 80 - 17 = 32 - 17 = 15\), which matches the right side, so \(x = 80\) is correct.

Yes. Multiply the whole equation by 5: 2x - 85 = 75, then solve 2x = 160, so x = 80.

Then \(\frac{2}{5x} = 32\), so \(5x = \frac{2}{32} = \frac{1}{16}\), giving \(x = \frac{1}{80}\).

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