4) Write an expression that is equi 4egroup the like terms. $$ \begin{aligned} \frac{1}{4} x+1+\frac{3}{4} x-\frac{2}{3}-\frac{1}{2} x & =\frac{1}{4} \ & =\end{aligned} $$

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UpStudy AI · Accepted Answer

Certainly! Let's simplify the given expression by grouping like terms.

**Original Expression:**
$$
\frac{1}{4}x + 1 + \frac{3}{4}x - \frac{2}{3} - \frac{1}{2}x
$$

**Step 1: Group Like Terms**

- **Combine the $$x$$-terms:**
  $$
  \frac{1}{4}x + \frac{3}{4}x - \frac{1}{2}x
  $$

- **Combine the constant terms:**
  $$
  1 - \frac{2}{3}
  $$

**Step 2: Simplify Each Group**

- **Simplify the $$x$$-terms:**
  $$
  \frac{1}{4}x + \frac{3}{4}x = \left(\frac{1}{4} + \frac{3}{4}\right)x = 1x
  $$
  $$
  1x - \frac{1}{2}x = \frac{1}{2}x
  $$

- **Simplify the constant terms:**
  $$
  1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}
  $$

**Step 3: Combine the Simplified Groups**

$$
\frac{1}{2}x + \frac{1}{3}
$$

**Final Simplified Expression:**
$$
\frac{1}{2}x + \frac{1}{3}
$$

This expression is equivalent to the original one, with like terms grouped and simplified.
$$ \frac{1}{2}x + \frac{1}{3} $$

Write an expression that is equi
4egroup the like terms.

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