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Consider the following equations and name the property of equality used to solve for the variable.

A. [tex]x + 3.75 = 7[/tex]

B. [tex]-3b = 18[/tex]

C. [tex]\frac{m}{5} = -25[/tex]

D. [tex]m - 4 = 9[/tex]


Sagot :

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
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