To find the missing reason, let's take a look at the steps leading up to it.
1. [tex]\(\frac{3}{2} x + 5 = -4\)[/tex] – This is the given equation.
2. [tex]\(3x + 10 = -8\)[/tex] – This result is achieved by multiplying both sides of the equation by 2. This is using the Multiplication Property of Equality.
3. [tex]\(3x = -18\)[/tex] – To go from [tex]\(3x + 10 = -8\)[/tex] to [tex]\(3x = -18\)[/tex], we subtract 10 from both sides of the equation. This is using the Subtraction Property of Equality.
4. [tex]\(x = -6\)[/tex] – To isolate [tex]\(x\)[/tex], the equation [tex]\(3x = -18\)[/tex] is divided by 3 on both sides. This uses the Division Property of Equality.
Since the step we are concerned with is from [tex]\(3x + 10 = -8\)[/tex] to [tex]\(3x = -18\)[/tex], the operation used is subtraction (subtracting 10 from both sides).
Therefore, the missing reason is:
b. Subtraction Property of Equality
