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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.

The table shows the steps for solving the given inequality for x 232x Select the reason for each step from the dropdown menus class=

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-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:

[tex]-2(3-2x)<x+3[/tex] Given,

[tex]-6+4x<x+3[/tex]: Distributive property,

[tex]-6+3x<3[/tex]: Subtraction property of order,

[tex]3x<9[/tex]: Addition property of order,

[tex]x<3[/tex]: Division property of order.

Step-by-step explanation:

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

[tex]-2(3-2x)<x+3[/tex]

Using distributive property, we will get:

[tex]-2\cdot3-(-2)\cdot2x<x+3[/tex]

[tex]-6+4x<x+3[/tex]

Subtract x from both sides:

[tex]-6+4x-x<x-x+3[/tex]

[tex]-6+3x<3[/tex]

Add 6 on both sides:

[tex]-6+6+3x<3+6[/tex]

[tex]3x<9[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}<\frac{9}{3}[/tex]

[tex]x<3[/tex]

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