Question

the equation sort
instructions:

1. analyze and solve the equations in the equation bank below.
2. determine if each equation has one solution, no solution, or infinitely many solutions.
3. write the letter of the equation into the correct column in the sorting table.

a, show work on the space provided.

equation bank
a. $3(x+2)=3x+6$
b. $4x-2=10$
c. $2x+5=2x+9$
d. $5x+10=5(x+2)$
e. $2(x-3)=2x+4$
f. $3x+5=2x+10$
g. $6x+3=3(2x+1)$
h. $x+4=x-2$
i. $2(x+4)=16$

Explanation:

Step1: Solve Equation A

Expand left side: $3(x+2)=3x+6$
Simplify: $3x+6=3x+6$
Subtract $3x$: $6=6$

Step2: Solve Equation B

Isolate $4x$: $4x=10+2$
Calculate: $4x=12$
Solve for $x$: $x=\frac{12}{4}=3$

Step3: Solve Equation C

Subtract $2x$: $5=9$

Step4: Solve Equation D

Expand right side: $5(x+2)=5x+10$
Simplify: $5x+10=5x+10$
Subtract $5x$: $10=10$

Step5: Solve Equation E

Expand left side: $2(x-3)=2x-6$
Simplify: $2x-6=2x+4$
Subtract $2x$: $-6=4$

Step6: Solve Equation F

Subtract $2x$: $x+5=10$
Solve for $x$: $x=10-5=5$

Step7: Solve Equation G

Expand right side: $3(2x+1)=6x+3$
Simplify: $6x+3=6x+3$
Subtract $6x$: $3=3$

Step8: Solve Equation H

Subtract $x$: $4=-2$

Step9: Solve Equation I

Expand left side: $2(x+4)=2x+8$
Simplify: $2x+8=16$
Isolate $2x$: $2x=16-8=8$
Solve for $x$: $x=\frac{8}{2}=4$

Answer:

One Solution:

B. $4x - 2 = 10$ (solution: $x=3$)
F. $3x + 5 = 2x + 10$ (solution: $x=5$)
I. $2(x + 4) = 16$ (solution: $x=4$)

No Solution:

C. $2x + 5 = 2x + 9$
E. $2(x - 3) = 2x + 4$
H. $x + 4 = x - 2$

Infinitely Many Solutions:

A. $3(x + 2) = 3x + 6$
D. $5x + 10 = 5(x + 2)$
G. $6x + 3 = 3(2x + 1)$