To identify which equation can be solved using the multiplication property of equality, let's analyze each one step by step:
1. [tex]\((x + 2)(x - 3) = 0\)[/tex]:
- This equation involves a product of two binomials equal to zero. To solve for [tex]\(x\)[/tex], we can use the zero product property, which states that if a product of two factors is zero, at least one of the factors must be zero. Therefore, we set each factor to zero:
[tex]\[
x + 2 = 0 \quad \text{or} \quad x - 3 = 0
\][/tex]
Solving these equations gives:
[tex]\[
x = -2 \quad \text{or} \quad x = 3
\][/tex]
This solution does not involve the multiplication property of equality.
2. [tex]\(m + 7 = -12\)[/tex]:
- This is a simple linear equation in which we can isolate [tex]\(m\)[/tex] by subtracting 7 from both sides:
[tex]\[
m + 7 - 7 = -12 - 7
\][/tex]
Simplifying this gives:
[tex]\[
m = -19
\][/tex]
This solution uses the addition/subtraction property of equality, not the multiplication property.
3. [tex]\(b \div (-2) = 18\)[/tex]:
- This equation can be solved using the multiplication property of equality. To isolate [tex]\(b\)[/tex], we multiply both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[
b \div (-2) \times (-2) = 18 \times (-2)
\][/tex]
Simplifying this gives:
[tex]\[
b = -36
\][/tex]
This process uses the multiplication property of equality, which maintains the equality by multiplying both sides of the equation by the same number.
4. [tex]\(-3 + y = 7\)[/tex]:
- This is another linear equation that can be solved using the addition/subtraction property of equality. To isolate [tex]\(y\)[/tex], we add 3 to both sides:
[tex]\[
-3 + y + 3 = 7 + 3
\][/tex]
Simplifying this gives:
[tex]\[
y = 10
\][/tex]
This solution does not involve the multiplication property of equality.
Considering the analysis above, the equation that can be solved using the multiplication property of equality is:
[tex]\[
b \div (-2) = 18
\][/tex]
