Question

PLLZ HELP! Solve each given equation and show your work. Tell whether it has on solution, and infinite number of solutions, or no solutions, and identify each equation as an identify, a contradiction, or neither.

(a) 2x + 3x - 6 = 10 + 4x

(b) 17 + 5x = 23 + 4x - 6 + x

(c) 7x + 4 = 5x + 8 + 2x - 10

Answer 1

a. 2x+3x-6=10+4x

5x-6=10+4x

5x-4x=10+6

x=16

one solution

b. 17+5x=23+4x-6+x

17+5x=17+5x

infinite number of solutions

c. 7x+4=5x+8+2x-10

7x+4=7x-2

no solution

Answer 2

(a) 2x + 3x - 6 = 10 + 4x ---> Answer: x = 16, it has one solution, it is an identity.

Adding the like terms on the same side of the equation to solve for x:

2x + 3x - 4x = 10 + 6

x = 16

(b) 17 + 5x = 23 + 4x - 6 + x ---> Answer: it has infinite number of solutions, it is a contradiction

Adding the like terms on the same side of the equation to solve for x:

5x - 4x - x = 23 - 17 - 6

5x - 5x = 6 - 6 (this equation is cancelling everything on each side so it can not be true no matter what value we assign, therefore it has infinite number of solution)

(c) 7x + 4 = 5x + 8 + 2x - 10 ---> Answer: no solution, its a contradiction.

Adding the like terms on the same side of the equation to solve for x:

7x - 5x - 2x = -10 + 8 - 4

7x - 7x = -6 (the terms of x are cancelled by each other, therefore no solution.