Question

Is 2 ( x - 1) + 18 equivalent to 6 (x + 3) - 4x - 6 used algebra to find your answer show your work and explain your answer 6th grade level

Answer 1

To determine if the two expressions \( 2 ( x - 1) + 18 \) and \( 6 (x + 3) - 4x - 6 \) are equivalent, we will simplify both expressions and see if they are equal.

### Step 1: Simplify the first expression

The first expression is:
\[
2 ( x - 1) + 18
\]
We start by distributing \(2\) to both terms inside the parentheses:
\[
= 2x - 2 + 18
\]
Next, we combine the constant terms \(-2\) and \(18\):
\[
= 2x + 16
\]

### Step 2: Simplify the second expression

The second expression is:
\[
6 (x + 3) - 4x - 6
\]
We start by distributing \(6\) to both terms inside the parentheses:
\[
= 6x + 18 - 4x - 6
\]
Next, we combine like terms. First, combine the \(6x\) and \(-4x\):
\[
= (6x - 4x) + (18 - 6)
\]
This simplifies to:
\[
= 2x + 12
\]

### Step 3: Compare the simplified expressions

Now we have:
- The first expression simplified to \( 2x + 16 \)
- The second expression simplified to \( 2x + 12 \)

These two results, \(2x + 16\) and \(2x + 12\), are not equal because \(16\) is not equal to \(12\).

### Conclusion

Therefore, the two expressions \( 2 ( x - 1) + 18 \) and \( 6 (x + 3) - 4x - 6 \) are **not equivalent**.