Question

Consider the equation x + 4 = 3x + 2.

a. Show that adding x + 2 to both sides of the equation does not change the solution set.
b. Show that multiplying both sides of the equation by x + 2 adds a second solution of x = -2 to the solution
set.

Answer 1

Explanation:

Given

(a)x+4=3x+2

x=1

adding x+2 both sides we get

x+4+x+2=3x+2+x+2

2x+6=4x+4

2x=2

x=1

so adding x+2 does not change solution of equation

(b)
`\left ( x+2\right )\left ( x+4\right )=\left ( 3x+2\right )\left ( x+2\right )`

`x^2+8+4x+2x=3x^2+6x+2x+4`

`=2x^2+2x-4`

`x^2+x-2=0`

`\left ( x-1\right )\left ( x+2\right )=0`

thus x=-2 adds in the solution of the Equation