Question

how many solutions does each equation have?
drag each equation to the correct category in the table. click on the reset button to start over.

number of solutions	equation
exactly one solution
infinitely many solutions

equations:
$4(m + 4) + 1 = 3(m + 6)$
$3(x + 4) = 3(x + 9)$
$6(a + 2) + 5 = 3 + 2(3a + 4) + 4a$

Explanation:

Step1: Simplify first equation

Expand and rearrange $4(x+3)+2=2(2x+7)$:
$4x+12+2=4x+14$
$4x+14=4x+14$
Subtract $4x$ from both sides: $14=14$

Step2: Simplify second equation

Expand and rearrange $2(x+4)=2(x+7)$:
$2x+8=2x+14$
Subtract $2x$ from both sides: $8=14$

Step3: Simplify third equation

Expand and rearrange $3(x+1)+5=2+3(2x+4)-3x$:
$3x+3+5=2+6x+12-3x$
$3x+8=3x+14$
Subtract $3x$ from both sides: $8=14$

Answer:

Number of Solutions	Equation
Exactly one solution	(None of the given equations)
Infinitely many solutions	$4(x+3)+2=2(2x+7)$