Question

Put the reasons into the correct order to justify solving the inequality: -2(x + 6) < 3(x + 1) -2x 12 < 3x + 3 -2x < 3x + 15 -5x < 15 x > 3 Justification 1 Justification 2 Justification 3 Justification 4 Justification 5 Division Property of Order Distributive Property Addition Property of Order Subtraction Property of Order Given​

Answer 1

The reasons put into the correct order to justify solving the inequality:

• -2(x + 6) < 3(x + 1) - Given
• -2x - 12 < 3x + 3 - Distributive Property
• -2x < 3x + 15 - Addition Property of Order
• -5x < 15 - Subtraction Property of Order
• x > 3 - Division Property of Order

Justify each property of equality

-2(x + 6) < 3(x + 1) - Given

-2x - 12 < 3x + 3 - Distributive Property

-2x < 3x + 15 - Addition Property of Order

-5x < 15 - Subtraction Property of Order

x > 3 - Division Property of Order

Check how to solve:

-2(x + 6) < 3(x + 1)

Open the parenthesis

-2x - 12 < 3x + 3

Add 12 to both sides

-2x - 12 + 12 < 3x + 3 + 12

-2x < 3x + 15

Subtract 3x from both sides

-2x - 3x < 3x + 15 - 3x

- 5x < 15

divide both sides by -5

x > 3

Therefore, the solution to the given inequality -2(x + 6) < 3(x + 1) is x > 3.

The properties mentioned above are properties of inequalities and hold for all situations of inequalities as given.

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