Question

determine whether each equation has no solution, exactly one solution, or infinitely many solutions. move the correct answer to each box. no solution exactly one solution infinitely many solutions 2x + 3 = 15 3x + 5 = 4x - x 7x - 4 = 9x - 4 - 2x

Explanation:

Step1: Solve $2x+3=15$

Subtract 3 from both sides:
$2x = 15 - 3$
$2x = 12$
Divide by 2:
$x = \frac{12}{2} = 6$
This has exactly one solution.

Step2: Solve $3x+5=4x-x$

Simplify right side:
$3x+5 = 3x$
Subtract $3x$ from both sides:
$5 = 0$
This is a false statement, so no solution.

Step3: Solve $7x-4=9x-4-2x$

Simplify right side:
$7x-4 = 7x-4$
Subtract $7x-4$ from both sides:
$0 = 0$
This is a true statement, so infinitely many solutions.

Answer:

$2x+3=15$ → Exactly one solution
$3x+5=4x-x$ → No solution
$7x-4=9x-4-2x$ → Infinitely many solutions