Question

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.4. show work on the space provided.equation banka. $3(x+2)=3x+6$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. $2(x+4)=16$sorting table:write the letter (e.g., \a\) of the equation in the correct column below.one solution$(x = \\#)$no solution(false statement)infinitely many(true statement)

Explanation:

Step1: Solve Equation A

Expand left side: $3(x+2)=3x+6$
Simplify: $3x+6=3x+6$
Subtract $3x+6$: $0=0$ (true statement)

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 $2x$: $5=9$ (false statement)

Step4: Solve Equation D

Expand right side: $5x+10=5x+10$
Subtract $5x+10$: $0=0$ (true statement)

Step5: Solve Equation E

Expand left side: $2x-6=2x+4$
Subtract $2x$: $-6=4$ (false statement)

Step6: Solve Equation F

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

Step7: Solve Equation G

Expand right side: $6x+3=6x+3$
Subtract $6x+3$: $0=0$ (true statement)

Step8: Solve Equation H

Subtract $x$: $4=-2$ (false statement)

Step9: Solve Equation I

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

Answer:

One Solution ($x=\#$)	No Solution (False Statement)	Infinitely Many (True Statement)
F. $3x + 5 = 2x + 10$ ($x=5$)	E. $2(x - 3) = 2x + 4$	D. $5x + 10 = 5(x + 2)$
I. $2(x + 4) = 16$ ($x=4$)	H. $x + 4 = x - 2$	G. $6x + 3 = 3(2x + 1)$