Question

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

−3(4 − 6x) < x + 5

Select the reason for each step from the drop-down menus.

–3(4 − 6x) < x + 5 ​ Given

−12 + 18x < x + 5 ​

−12 + 17x < 5 ​ Subtraction Property of Order

​ 17 x < 17

x < 1

Answer 1

We are given :  -3(4-6x) < x+5.

Solution: -3 is in front of Parenthesis.

We need to multiply -3 by (4-6x).

So, we need to applying distributive property.

On distributing, we get

-12+18x < x+5        (By distributive property)

The reverse operation of addition is subtraction. So we need to subtract x from both sides, we get

-12+18x-x < x-x+5    (By subtraction property of equality).

-12+17x < 5

Now, we need to get rid -12 from left side.

So, we need to apply addition property of equality, we need to add 12 on both sides, we get

-12+12+18x < x+5+12    (By addition property of equality)

17x < 17

We need to get rid 17 from left side. So we need to apply division property of equality.

On dividing both sides by 17, we get

17x/17 < 17/17      (By division property of equality)

x < 1.