Question

The table shows the steps for solving the given inequality for x.

−2(3−2x)
Select the reason for each step from the drop-down menus.

Answer 1

-6 + 4x < x +3 : Distributive property

-6 + 3x < 3 : Subtraction property of inequality

3x < 9 : Addition property of inequality

x <3 : Division property of inequality

Answer 2

`-2(3-2x)<x+3` Given,

`-6+4x<x+3`: Distributive property,

`-6+3x<3`: Subtraction property of order,

`3x<9`: Addition property of order,

`x<3`: Division property of order.

Explanation:

We have been given an inequality. We are asked to match each step for solving the equation with reason.

`-2(3-2x)<x+3`

Using distributive property, we will get:

`-2\cdot3-(-2)\cdot2x<x+3`

`-6+4x<x+3`

Subtract x from both sides:

`-6+4x-x<x-x+3`

`-6+3x<3`

Add 6 on both sides:

`-6+6+3x<3+6`

`3x<9`

Divide both sides by 3:

`(3x)/(3)<(9)/(3)`

`x<3`