Core Connections: Course 3
CC
Core Connections: Course 3 View details
2. Section 3.2
Continue to next subchapter

Exercise 75 Page 125

Practice makes perfect
We are given an equation and asked to check if a given solution, x=- 4, is correct. 3x+7=x-1 To check if x=- 4 is a correct solution, we should substitute - 4 for x in the given equation and simplify to check if we get an identity or a contradiction.

3x+7=x-1
3( - 4)+7? = - 4-1
- 12+7? =- 4-1
- 5= - 5 ✓

Simplifying the expression resulted in an identity. Therefore, x=- 4 is a correct solution.

In this case, we are given an equation and asked to check if a given solution, x=3, is correct. - 2x-4=- 4x+3 To check if x=3 is a correct solution, we should substitute 3 for x in the given equation and simplify to check if we get an identity or a contradiction.

- 2x-4=- 4x+3
- 2( 3)-4? =- 4( 3)+3
- 6-4? =- 12+3
- 10≠ - 9 *

Simplifying the expression resulted in a contradiction. Therefore, x=3 is not a correct solution.

In this case, we are given an equation and asked to check if a given solution, x=2, is correct. - 3x+5+5x-1=0 To check if x=2 is a correct solution, we should substitute 2 for x in the given equation and simplify to check if we get an identity or a contradiction.

- 3x+5+5x-1=0
- 3( 2)+5+5( 2)-1? =0
- 6+5+10-1? =0
8≠ 0 *

Simplifying the expression resulted in a contradiction. Therefore, x=2 is not a correct solution.

In this case, we are given an equation and asked to check if a given solution, x=3, is correct. - (x-1) = 4x-5-3x To check if x=3 is a correct solution, we should substitute 3 for x in the given equation and simplify to check if we get an identity or a contradiction.

- (x-1) = 4x-5-3x
- ( 3-1) ? = 4( 3)-5-3( 3)
- (3-1) ? = 12-5-9
- 2 = - 2 ✓

Simplifying the expression resulted in an identity. Therefore, x=3 is a correct solution.