Question

For problems 3 and 4, state whether the given values of c and d create an equation with only one

solution, infinitely many solutions, or no solution.
3, 5x+2= cx + d
a. c= 5, d=5
b. c= 5, d=2
c. c = 2, d = 5

Answer 1

a. No solutions

Substitute the Cs inside for 5 and Ds inside for 5.

5x + 2 = 5x + 5

Solve:

Subtract 5x from both sides

2 ≠ 5

Therefore, the answer for a is no solutions.

b. Infinitely many solutions

Now let’s substitute the Cs for 5 and the Ds for 2.

5x + 2 = 5x + 2

Solve:

Subtract 5x from both sides

2 = 2

So, the answer for b is infinitely many solutions

c. One solution

Let’s substitute the Cs for 2 and the Ds for 5.

5x + 2 = 2x + 5

Solve:

Subtract 2x from both sides

3x + 2 = 5

Now subtract 2 from both sides

3x = 3

Divide both sides by 3

x = 1

So the answer for c would be one solution.