Question

From first to last order the steps to provide the expression a is equivalent to expression b expression a ( x + 4 * x - 2 expression b x squared plus 2x - 8

Answer 1

To determine whether expression \( a \) is equivalent to expression \( b \) and to transform \( a \) to \( b \), we need to simplify and manipulate the expression step by step. However, the expressions need to be clarified a bit as you have presented them. Let's assume the expressions are:

- Expression \( a \): \( x + 4x - 2 \)
- Expression \( b \): \( x^2 + 2x - 8 \)

### Steps to Transform Expression \( a \) into Expression \( b \)

1. **Combine Like Terms in Expression \( a \)**:
\[
a = x + 4x - 2 = 5x - 2
\]

2. **Set Up an Equation to Check for Equivalence**:
We want to check if \( 5x - 2 \) is equivalent to \( x^2 + 2x - 8 \). We'll set the expressions equal to each other:
\[
5x - 2 = x^2 + 2x - 8
\]

3. **Rearrange the Equation**:
Move all terms to one side of the equation:
\[
0 = x^2 + 2x - 8 - 5x + 2
\]
Which simplifies to:
\[
0 = x^2 - 3x - 6
\]

4. **Formulate as a Standard Quadratic Equation**:
Rearranging the above, we have:
\[
x^2 - 3x - 6 = 0
\]

5. **Check for Roots (Factoring or Using Quadratic Formula)**:
This equation can be factored or solved using the quadratic formula:
- The discriminant \( D = b^2 - 4ac \) for \( a=1, b=-3, c=-6 \):
\[
D = (-3)^2 - 4(1)(-6) = 9 + 24 = 33
\]
Since the discriminant is positive, there are two real roots.

6. **Find the Roots Using Quadratic Formula**:
\[
x = \frac{-b \pm \sqrt{D}}{2a} = \frac{3 \pm \sqrt{33}}{2}
\]
These roots show that \( a \) and \( b \) are not equivalent for all \( x \).

### Conclusion
After analyzing both expressions, we find that \( a = 5x - 2 \) is not equivalent to \( b = x^2 + 2x - 8 \), as they produce different outputs given the same input values of \( x \).

If the expressions \( a \) and \( b \) you were referring to are different, please clarify, and I can assist you in verifying their equivalence!