Question

What is a number line for 5a + 18 < -27?

Answer 1

Answer:

Letter C.

Step-by-step explanation:

Let’s start by subtracting \blue{18}18start color #6495ed, 18, end color #6495ed from both sides of the inequality:

\qquad \begin{aligned} 5a + 18 &< -27\\ 5a + 18 \blue{-18} &< -27\blue{-18}\\ 5a &< -45\\ \end{aligned}

5a+18

5a+18−18

5a​  

<−27

<−27−18

<−45

Hint #22 / 4

To isolate aaa, we need to divide both sides by \green{5}5start color #28ae7b, 5, end color #28ae7b:

\qquad\begin{aligned} 5a &< -45\\ \\ \dfrac{5a}{\green{5}} &< \dfrac{-45}{\green{5}}\\ \\ a &< \purple{-9}\\ \end{aligned}

5a

5

5a

a

<−45

<

5

−45

<−9

​Hint #33 / 4

To graph the inequality a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd, we first draw a circle at \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd. This circle divides the number line into two sections: one that contains solutions to the inequality and one that does not.

Since the solution uses a less than sign, the solution does not include the point where a= \purple{-9}a=−9a, equals, start color #9d38bd, minus, 9, end color #9d38bd. So the circle at \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd is not filled in.

Because the solution to the inequality says that a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd, this means that solutions are numbers to the left of \purple{-9}−9start color #9d38bd, minus, 9, end color #9d38bd.

Hint #44 / 4

The graph that represents the solution of the inequality a < \purple{-9}a<−9a, is less than, start color #9d38bd, minus, 9, end color #9d38bd is shown in

Answer 2

a < -9

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    5*a+18-(-27)<0  

Step by step solution :

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  5a + 45  =   5 • (a + 9)  

Equation at the end of step  1  :

Step  2  :

2.1    Divide both sides by  5  

Solve Basic Inequality :

2.2      Subtract  9  from both sides

           a < -9