Question

match each equation to the number of solutions it has:a. $6(x - 4)+10x = 16x - 28$b. $11x + 4 + x = 12x + 4$c. $11x + 4 - 7x = 5x + 4$d. $12x - 3 + x - 2 = 13x - 5$no solutionone solutioninfinite solutions

Explanation:

Step1: Simplify Equation A

Expand and combine like terms:
$6(x-4)+10x = 6x - 24 + 10x = 16x - 24$
Set equal to right side: $16x - 24 = 16x - 28$
Subtract $16x$ from both sides: $-24 = -28$ (false)

Step2: Simplify Equation B

Combine like terms on left:
$11x + 4 + x = 12x + 4$
Set equal to right side: $12x + 4 = 12x + 4$
Subtract $12x + 4$ from both sides: $0 = 0$ (always true)

Step3: Simplify Equation C

Combine like terms on left:
$11x + 4 - 7x = 4x + 4$
Set equal to right side: $4x + 4 = 5x + 4$
Subtract $4x + 4$ from both sides: $0 = x$ (single solution)

Step4: Simplify Equation D

Combine like terms on left:
$12x - 3 + x - 2 = 13x - 5$
Set equal to right side: $13x - 5 = 13x - 5$
Subtract $13x - 5$ from both sides: $0 = 0$ (always true)

Answer:

• A. $6(x - 4) + 10x = 16x - 28$: No solution
• B. $11x + 4 + x = 12x + 4$: Infinite solutions
• C. $11x + 4 - 7x = 5x + 4$: One solution
• D. $12x - 3 + x - 2 = 13x - 5$: Infinite solutions