Question

Solve each given equation and show your work tell whether each equation has one solution infinite number of solutions or no Solutions.

(a) 2x+4(x-1)=2+4x
(b) 25-x=15-(3x+10)
(c) 4x=2x+2x+5(x-x)

Answer 1

(a) x = 3, one solution

(b) x = -10, one solution

(c) infinite solutions

Explanation:

In each case, we can subtract the right side from both sides and simplify.

(a)

(2x +4(x -1)) -(2 +4x) = 0

2x +4x -4 -2 -4x = 0 . . . . . . eliminate parentheses

2x -6 = 0 . . . . . . . . . . . . . . . collect terms

x - 3 = 0 . . . . . . . . . . . . . . . . divide by 2

x = 3 . . . . . . . . . . . . . . . . . . . add 3, one solution

__

(b)

25 -x -(15 -(3x +10)) = 0

25 -x -15 +3x +10 = 0 . . . . . . eliminate parentheses

2x +20 = 0 . . . . . . . . . . . . . . .collect terms

x +10 = 0 . . . . . . . . . . . . . . . . divide by 2

x = -10 . . . . . . . . . . . . . . . . . . add -10, one solution

__

(c)

4x - (2x+2x+5(x-x)) = 0

4x -2x -2x +0 = 0

0 = 0 . . . . . . . . . . . . . . . . . . . true for all values of x, infinite solutions