Question

To solve the equation 3x-7=x-2, Alex says the first step is to subtract x from both sides. Danny says the first step is to add 7 to both sides.

a.Solve the equation using Alex's method of first subtracting x from both sides.

b.Solve the equation using Danny's method of first adding 7 to both sides.

c.Who is correct, Alex or Danny? Justify your answer.

d. Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.

Answer 1

B I’m thinking ......

Answer 2

`x=(5)/(2)`

Explanation:

Given : Equation
`3x-7=x-2`

To find : Solve the equation ?

Solution :

a) Solve the equation using Alex's method of first subtracting x from both sides.

Equation
`3x-7=x-2`

Subtract x from both side,

`3x-7-x=x-2-x`

`2x-7=-2`

`2x=-2+7`

`2x=5`

`x=(5)/(2)`

b) Solve the equation using Danny's method of first adding 7 to both sides.

Equation
`3x-7=x-2`

Adding 7 from both side,

`3x-7+7=x-2+7`

`3x=x+5`

`2x=5`

`x=(5)/(2)`

c) Both are correct in their ways.

d) Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.

Equation
`3x-7=x-2`

We can isolate the terms as like terms place together,

`3x-x=-2+7`

`2x=5`

`x=(5)/(2)`