Sure, let's solve each equation step-by-step and identify the property of equality used:
### A. [tex]\( x + 3.75 = 7 \)[/tex]
1. Equation: [tex]\( x + 3.75 = 7 \)[/tex]
2. Step: Subtract 3.75 from both sides.
[tex]\[
x + 3.75 - 3.75 = 7 - 3.75
\][/tex]
3. Simplify: [tex]\( x = 3.25 \)[/tex]
Property of equality used: Subtraction Property of Equality
### B. [tex]\( -3b = 18 \)[/tex]
1. Equation: [tex]\( -3b = 18 \)[/tex]
2. Step: Divide both sides by -3.
[tex]\[
\frac{-3b}{-3} = \frac{18}{-3}
\][/tex]
3. Simplify: [tex]\( b = -6 \)[/tex]
Property of equality used: Division Property of Equality
### C. [tex]\( \frac{m}{5} = -25 \)[/tex]
1. Equation: [tex]\( \frac{m}{5} = -25 \)[/tex]
2. Step: Multiply both sides by 5.
[tex]\[
\left( \frac{m}{5} \right) \times 5 = -25 \times 5
\][/tex]
3. Simplify: [tex]\( m = -125 \)[/tex]
Property of equality used: Multiplication Property of Equality
### D. [tex]\( m - 4 = 9 \)[/tex]
1. Equation: [tex]\( m - 4 = 9 \)[/tex]
2. Step: Add 4 to both sides.
[tex]\[
m - 4 + 4 = 9 + 4
\][/tex]
3. Simplify: [tex]\( m = 13 \)[/tex]
Property of equality used: Addition Property of Equality
### Summary:
For the equations [tex]\( x + 3.75 = 7 \)[/tex], [tex]\( -3b = 18 \)[/tex], [tex]\( \frac{m}{5} = -25 \)[/tex], and [tex]\( m - 4 = 9 \)[/tex], the solutions and respective properties of equality used are as follows:
- A. Solution: [tex]\( x = 3.25 \)[/tex], Property: Subtraction Property of Equality
- B. Solution: [tex]\( b = -6 \)[/tex], Property: Division Property of Equality
- C. Solution: [tex]\( m = -125 \)[/tex], Property: Multiplication Property of Equality
- D. Solution: [tex]\( m = 13 \)[/tex], Property: Addition Property of Equality
