Question

1. solve the equation 3(x + 1) = 27. write a reason for each numbered step.

3(x + 1) = 27 given
3x + 3 = 27 1
-3 -3 subtraction property of equality
3x = 24 simplify.
(3x)/3 = 24/3 2
x = 8 simplify.

a. 1 multiplication property of equality; 2 division property of equality
b. 1 distributive property; 2 division property of equality
c. 1 division property of equality; 2 addition property of equality
d. 1 distributive property; 2 multiplication property of equality

1. you want to know the number of minutes that you can use on your $45.00 phone card. the card company charges you $0.50 for the first minute and $0.05 for each additional minute. solve the formula $45.00 = $0.50 + $0.05m for m. justify each step with an algebraic property of equality.

Explanation:

Step1: Analyze Step [1]

To get from \( 3(x + 1)=27 \) to \( 3x + 3 = 27 \), we use the Distributive Property, which states that \( a(b + c)=ab+ac \). Here, \( a = 3 \), \( b=x \), and \( c = 1 \), so \( 3(x + 1)=3x+3 \).

Step2: Analyze Step [2]

To get from \( 3x=24 \) to \( \frac{3x}{3}=\frac{24}{3} \), we use the Division Property of Equality, which states that if \( a = b \), then \( \frac{a}{c}=\frac{b}{c} \) (where \( c
eq0 \)). Here, we divide both sides by 3.

Step3: Evaluate Options

• Option a: [1] is not Multiplication Property, so a is wrong.
• Option b: [1] is Distributive Property, [2] is Division Property of Equality, which matches our analysis.
• Option c: [1] is not Division Property, [2] is not Addition Property, so c is wrong.
• Option d: [2] is not Multiplication Property, so d is wrong.

Answer:

b. [1] Distributive Property; [2] Division Property of Equality