Question

c. \\(\frac{1}{2}x = 50 - \frac{3}{4}x\\)

Explanation:

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<reasoning>

Add term to both sides

Using the Multi-Step Equations and Combining Like Terms knowledge points
\[

$$\begin{aligned} \frac{1}{2}x &= 50 - \frac{3}{4}x \\ \frac{1}{2}x + \frac{3}{4}x &= 50 \end{aligned}$$

\]

Combine variable terms

Using the Combining Like Terms knowledge point
\[

$$\begin{aligned} \frac{2}{4}x + \frac{3}{4}x &= 50 \\ \frac{5}{4}x &= 50 \end{aligned}$$

\]

Solve for x

Using the Multiplication Property of Equality knowledge point
\[

$$\begin{aligned} x &= 50 \cdot \frac{4}{5} \\ x &= 40 \end{aligned}$$

\]

</reasoning>

<answer>
c. \(\frac{1}{2}x = 50 - \frac{3}{4}x\)
\(x =\) <blank>\(40\)</blank>
</answer>

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Answer:

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<reasoning>

Add term to both sides

Using the Multi-Step Equations and Combining Like Terms knowledge points
\[

$$\begin{aligned} \frac{1}{2}x &= 50 - \frac{3}{4}x \\ \frac{1}{2}x + \frac{3}{4}x &= 50 \end{aligned}$$

\]

Combine variable terms

Using the Combining Like Terms knowledge point
\[

$$\begin{aligned} \frac{2}{4}x + \frac{3}{4}x &= 50 \\ \frac{5}{4}x &= 50 \end{aligned}$$

\]

Solve for x

Using the Multiplication Property of Equality knowledge point
\[

$$\begin{aligned} x &= 50 \cdot \frac{4}{5} \\ x &= 40 \end{aligned}$$

\]

</reasoning>

<answer>
c. \(\frac{1}{2}x = 50 - \frac{3}{4}x\)
\(x =\) <blank>\(40\)</blank>
</answer>

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