Question

What is the missing step in solving the inequality 4(x – 3) + 4 = 10 +6X?

1. The distributive property: 4x - 12 + 4 < 10 + 6x

2. Combine like terms: 4x -8 <10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: -2x < 18

5. The division property of inequality

xs-9

OX-9

Answer 1

Divide both sides of the inequality by -2:

`(-2x)/(-2)>(18)/(-2)\\\\x>-9`

Explanation:

The Division property of Inequality states that:

`If\ c>0\ and\ a>b,then\ (a)/(c)> (b)/(c)\\\\If\ c>0\ and\ a<b,then\ (a)/(c)< (b)/(c)\\\\\\If\ c<0\ and\ a>b,then\ (a)/(c)< (b)/(c)\\\\If\ c<0\ and\ a<b,then\ (a)/(c)>(b)/(c)`

Therefore, given the inequality:

`4(x - 3) + 4 < 10 + 6x`

The missing step in solving it, applying the Division property of inequality, is divide both sides of the inequality by -2:

`(-2x)/(-2)>(18)/(-2)\\\\x>-9`