Ariel needs to solve this equation for x.

$$3x\ -\ 7\ =\ 11$$  

What would be the best first step Ariel could make to solve the equation?

Karen solve an equation incorrectly as shown below.

Given: 4(x + 1) - 3(x -2) = 11

Step 1: 4x + 4 - 3x + 6 = 11

Step 2: 4x - 3x + 4 + 6 = 11

Step 3: x + 10 = 11

Step 4: x + 10 + 10 = 11 + 10

Answer: x = 21

Jared solved the equation shown below.

Given: 5(x + 1) - 3(x -2) = 13

Step 1: 5x + 5 - 3x + 6 = 13

Step 2: 5x - 3x + 5 + 6 = 13

Step 3: 2x + 11 = 13

Step 4: 2x + 11 - 11 = 13 - 11

Step 5: 2x = 2

Answer: x = 1

Which properties did he apply from step 1 to step 2?

Lisa completes the steps for solving this linear equation for x.

Original equation: $$\frac{1}{2}\left(x+6\right)\ =\ -\frac{3}{2}x+5$$  

Step 1: $$\frac{1}{2}x+3\ =-\frac{3}{2}x+5$$  

Step 2: 2x + 3= 5

Step 3: 2x = 2

Step 4: x =1

Step 5: 2x = 2

Answer: x = 1

Which properties did he apply from step 1 to step 2?

Jill solved the equation below.

$$2\left(x\ -1\right)\ =\ x\ +12$$  

$$2x\ -\ 2\ =\ x+12$$  

$$x-2=\ 12$$  

$$x=14$$  

She applied three properties of equality: I. Addition property of equality, II. Subtraction property of equality and III. Distributive property. In which order did Jill use the properties?

Find the error