1/2x-y,x+3/4-z,x/2+y/2+z/2 add the following

We are asked to add the following three expressions:

1. \( \frac{1}{2}x - y \)
2. \( x + \frac{3}{4} - z \)
3. \( \frac{x}{2} + \frac{y}{2} + \frac{z}{2} \)

### Step-by-Step Solution:

We will add these three expressions by grouping like terms (i.e., terms with the same variables: \(x\), \(y\), and \(z\), and the constant terms).

1. **For \(x\)-terms**:
   - First expression: \( \frac{1}{2}x \)
   - Second expression: \( x \)
   - Third expression: \( \frac{x}{2} \)

   Summing them:
   \[
   \frac{1}{2}x + x + \frac{x}{2} = \frac{1}{2}x + \frac{2}{2}x + \frac{1}{2}x = 2x
   \]

2. **For \(y\)-terms**:
   - First expression: \(-y\)
   - Second expression: no \(y\)-term
   - Third expression: \( \frac{y}{2} \)

   Summing them:
   \[
   -y + \frac{y}{2} = -\frac{2}{2}y + \frac{1}{2}y = -\frac{1}{2}y
   \]

3. **For \(z\)-terms**:
   - First expression: no \(z\)-term
   - Second expression: \(-z\)
   - Third expression: \( \frac{z}{2} \)

   Summing them:
   \[
   -z + \frac{z}{2} = -\frac{2}{2}z + \frac{1}{2}z = -\frac{1}{2}z
   \]

4. **For constant terms**:
   - First expression: no constant term
   - Second expression: \( \frac{3}{4} \)
   - Third expression: no constant term

   The constant term remains \( \frac{3}{4} \).

### Final Result:
\[
2x - \frac{1}{2}y - \frac{1}{2}z + \frac{3}{4}
\]

This is the result of adding the three expressions together.

Would you like further details or have any questions?

Here are 5 questions to consider:
1. How do you combine fractions with different denominators?
2. Can you add or subtract terms with different variables?
3. What are like terms and how do they simplify an expression?
4. How would the result change if the coefficients of \(x\), \(y\), or \(z\) were different?
5. What happens if you have to subtract rather than add expressions?

**Tip:** Always align similar terms when simplifying algebraic expressions to avoid confusion.

1/2x-y, x+3/4-z, x/2+y/2+z/2 add the following

Learn how to add the linear expressions 1/2x - y, x + 3/4 - z, and x/2 + y/2 + z/2 with a clear, step-by-step solution. This algebra problem involves adding like terms and simplifying expressions. Suitable for students in Grades 6-8.

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