Question

What is the expression 4+8(3x−2)−7x
4
+
8
(
3
𝑥
−
2
)
−
7
𝑥
when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.(4 points)
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Answer 1

write in word form so i can copy and paste

Answer 2

write it in explanation

Answer 3

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations and apply the distributive property. Here are the steps:

1. **Distribute \(8\) through the parentheses**:
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]
Now, replace \(8(3x - 2)\) in the original expression:
\[
4 + (24x - 16) - 7x
\]

2. **Combine like terms**:
- First, we can simplify the constant terms \(4\) and \(-16\):
\[
4 - 16 = -12
\]
- Next, combine the \(x\) terms \(24x\) and \(-7x\):
\[
24x - 7x = 17x
\]

3. **Put it all together**:
Now we rewrite the expression:
\[
-12 + 17x
\]
To keep it in a conventional order (typically showing the \(x\) term first), we can rearrange it:
\[
17x - 12
\]

So, the simplified expression is:
\[
\boxed{17x - 12}
\]

Answer 4

Seventeen x minus twelve.

Answer 5

The expression \( 4 + 8(3x - 2) - 7x \) simplifies to **seventeen x minus twelve**.

To reach this result, we first applied the distributive property to the expression \( 8(3x - 2) \), which resulted in \( 24x - 16 \). We then combined the constant terms \( 4 \) and \( -16 \) to get \( -12 \) and combined the \( x \) terms \( 24x \) and \( -7x \) to obtain \( 17x \). Finally, we rewrote the expression to present it in standard form, which is **seventeen x minus twelve**.