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

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

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: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq