Question

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

a) 20-4x=12-x+8-3x

b) 5x+4x-3=24+8x

c) 5x+6=2x+6+3x-15

Answer 1

Explanation:

a) 20 - 4x = 12 - x + 8 - 3x

• 20 - 4x = 12 + 8 - x - 3x
• 20 - 4x = 20 - 4x
• x has an infinite number of solutions
• identity

b) 5x + 4x - 3 = 24 + 8x

• 9x - 3 = 24 + 8x
• 9x - 8x - 3 = 24 + 8x - 8x
• x - 3 = 24
• x - 3 + 3 = 24 + 3
• x = 27
• x has one solution
• neither

c) 5x + 6 = 2x + 6 + 3x - 15

• 5x + 6 - 2x = 2x + 6 + 3x - 15 - 2x
• 3x + 6 = 6 + 3x - 15
• 3x + 6 - 3x = 6 + 3x - 15 - 3x
• 6 = 6 - 15
• no solution
• contradiction