Question

evaluate each expression if ( a = 3, b = 5, ) and ( c = 1. )

1. ( b - c )
2. ( ac + b )
3. ( \frac{2(b + c)}{a} )

use the distributive property to evaluate each expression.

1. ( 4(9 + 1) )
2. ( -5(6 + x) )

name the property shown by each statement.

1. ( c \times 1 = c )
2. ( 83 + (52 + 17) = (83 + 52) + 17 )
3. ( 22 + b + 18 = b + 22 + 18 )

Explanation:

Problem 1: \( b - c \)

Step1: Substitute values of \( b \) and \( c \)

Given \( b = 5 \) and \( c = 1 \), substitute into the expression: \( 5 - 1 \)

Step2: Perform the subtraction

\( 5 - 1 = 4 \)

Step1: Substitute values of \( a \), \( c \), and \( b \)

Given \( a = 3 \), \( c = 1 \), \( b = 5 \), substitute into the expression: \( 3\times1 + 5 \)

Step2: Perform the multiplication and addition

First, \( 3\times1 = 3 \), then \( 3 + 5 = 8 \)

Step1: Substitute values of \( a \), \( b \), and \( c \)

Given \( a = 3 \), \( b = 5 \), \( c = 1 \), substitute into the expression: \( \frac{2(5 + 1)}{3} \)

Step2: Simplify the numerator

First, calculate \( 5 + 1 = 6 \), then \( 2\times6 = 12 \), so the expression becomes \( \frac{12}{3} \)

Step3: Perform the division

\( \frac{12}{3} = 4 \)

Answer:

\( 4 \)

Problem 2: \( ac + b \)