Question

What is the expression 4+8(3x−2)−7x
when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.

for 7th grade

Answer 1

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations (also known as PEMDAS/BODMAS) and apply the distributive property.

1. **Distribute \( 8 \) to both terms inside the parentheses \( (3x - 2) \):**
\[
8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16
\]

2. **Substitute this back into the original expression:**
\[
4 + (24x - 16) - 7x
\]

3. **Now combine like terms. Start with the constants (the numbers) and then the variable terms (the terms with \( x \)):**
- Constants: \( 4 - 16 = -12 \)
- Variable terms: \( 24x - 7x = 17x \)

4. **Putting it all together:**
\[
-12 + 17x
\]

5. **Rearranging the expression for clarity (usually with the variable first):**
\[
17x - 12
\]

So, the expression \( 4 + 8(3x - 2) - 7x \) simplifies to \( \boxed{17x - 12} \).