Solve each inequality, graph each solution, and give interval notation.

Question

(a+4)-3(a+1)>-2(1-a)-5

 

 

 

 

 

Answer 1

We solve an inequality the same way we solve an equation.

 

(a + 4) - 3(a + 1) > -2(1 - a) - 5

 

 

First, we distribute terms to get rid of parentheses.

 

a + 4 - 3a - 3 > -2 + 2a - 5

 

 

Combine like terms on each side of inequality.

 

-2a + 1 > 2a - 7

 

 

Subtract 2a on both sides of inequality.

 

-4a + 1 > -7

 

 

Subtract 1 on both sides of inequality.

 

-4a > -8

 

 

Divide both sides by -4.

 

a > 2

 

 

When we divide by a negative coefficient in an inequality, we flip the inequality sign.

 

a < 2

 

 

In interval notation,
 
(-∞, 2)

 

 

The solution is all values of a less than 2.