L3.5 Determining Number of Solution

Infinite Solution, No Solution, or One Solution

100

3(2x+5)−4=6x+11

6x + 11 = 6x + 11

7 = 7

Infinite Solutions

200

7(2x−1)+3x=17x−6

17x - 7 = 17x - 6

-7 = -6

No Solution

300

3(2x+4)−5=6x+8

6x + 7 = 6x + 8

7 = 8

No solution

400

4(x−3)+2=2(2x−4)−2

4x - 10 = 4x - 10

-10 = -10

Infinite Solution

500

5(2x+3)=10x+20

10x + 15 = 10x + 20

15 = 20

No Solution

Infinite Solution, No Solution, or One Solution

100

5(3x+2)−4x=11x+12+x

11x + 10 = 12x + 12

x = -2

One Solution

200

4(2x+3)−5=3x+12

8x + 3 = 3x + 18

x = 3

One Solution

300

5(3x+1)−4x=10x+5+x

11x + 5= 11x + 5

5 = 5

Infinite Solution

400

4(x−3)+6=4x−9

4x - 6 = 4x - 9

-6 = -9

No Solution

500

8(2x−1)+2x=18x−8

18x - 8 = 18x - 8

-8 = -8

Infinite Solution

Complete each equation so that it has infinitely many solutions.

100

3(2x + 4) − 5 = _____x + _____

6x + 7

200

4(x − 3) + 2 = _____x + _____

4x + 10

300

5(3x−2)−x = _____x +_____

14x−10

400

7(2x − 7) − 8x = _____x + _____

6x − 49

500

6(3x − 2) + 2x − 7 = _____x + _____

20x − 19

Complete each equation so that it has no solutions.

100

-4(2x + 5) − 3 = _____x + _____

-8x + _____

=/ -23

200

5(3x + 1) − 6x + 8 = _____x + _____

9x + _____

=/ 13

300

-7(x − 4) + 2x = _____x + _____

-5x + _____

=/ 28

400

2(4x − 7) + 9  = _____x + _____

8x + _____

=/ -5

500

3(2x+4)−x−5 = _____x + _____

5x + _____

=/ 7