2(2x + 5) = 4(x + 3)

A.

one solution

B.

infinite solutions

C.

no solution

2. How many solutions does the equation have?

a + 5 = 1/5 (5a + 25)

A.

one solution

B.

infinite solutions

C.

no solution

3. How many solutions does the equation have?

3(4x - 3) - 7x = 5x - 9

A.

one solution

B.

infinite solutions

C.

no solution

4.

Which expressions would complete this equation so that it has infinitely many solutions?

8 + 2(8x – 6) =

Choose exactly two answers that are correct.

A.

2(4x + 7)

B.

9x – 10

C.

16x – 4

D.

4(4x – 1)

Match each item in Column A to an answer in Column B.

5.

(1 pt)

What is the best way to classify each equation?

Column A Column B

1. 8x + 24 = 2(4x + 12) A. identity

2. 5x + 18 - x = 2(2x + 8) B. contradiction

3. 7(3x - 2) = 20x - 13 C. neither

4. 3x + 2(x - 10) = 5(x - 4)

1.) Let’s solve for x.

2(2x + 5) = 4(x + 3)

4x + 10 = 4x + 12

4x - 4x = 12 - 10

0 = 2

Since we can’t solve for x and also the argument is not true that 0 is not equal to 2. Therefore, NO SOLUTION (C).

2.) Let’s solve for x.

a + 5 = 1/5 (5a + 25)

a + 5 = a + 5

a - a = 5 - 5

0 = 0

Since we can’t solve for x but the argument is true which zero is equal to zero. This case becomes "indeterminate" because 0/1 = 0, 0/2 = 0, 0/3 = 0 and so on. Therefore, the answer is INFINITE SOLUTIONS (B).

3) Let’s solve for x.

3(4x - 3) - 7x = 5x - 9

12x - 9 - 7x = 5x - 9

5x - 9 = 5x - 9

5x - 5x = -9 + 9

0 = 0

Therefore, INFINITE SOLUTIONS (B).

4.) Let’s test each choices if the solution does not exist.

a. ) 8 + 2(8x – 6) = 2(4x - 7)

8 + 16x -12 = 8x - 14

16x - 8x = -14 - 8 + 12

8x = -10

x = -1.25 (one solution)

b. ) 8 + 2(8x – 6) = 9x - 19

8 + 16x - 12 = 9x - 19

16x - 9x = -19 - 8 + 12

7x = -15

x = -15/7 (one solution)

c. ) 8 + 2(8x – 6) = 16x - 4

8 + 16x - 12 = 16x - 4

16x - 16x = -4 - 8 + 12

0 = 0 (infinite solutions)

d. ) 8 + 2(8x – 6) = 4(4x -1)

8 + 16x - 12 = 16x - 4

16x - 16x = -4 - 8 + 12

0 = 0 (infinite solutions)

Therefore, the answers are C and D.

5.) Since we know how to solve for x, I am gonna conclude the answer instead. Identity is another term of "one solution". Contradiction is another term of "no solution". Neither is considered as "infinite solutions. "

Number 1 is NEITHER.

Number 2 is CONTRADICTION.

Number 3 is IDENTITY.

Number 4 is NEITHER.