Question

Solve and graph the following inequality (say if the number line is opened or closed):

−5a+17<62
(1 point)
Responses

Answer 1

you say shade everything to the right but why did you make the number line point left?

Answer 2

To solve this inequality, we need to isolate the variable a on one side of the inequality sign.

-5a + 17 < 62

We can start by subtracting 17 from both sides:

-5a < 62 - 17
-5a < 45

Next, we divide both sides by -5. Since we are dividing by a negative number, the inequality sign will change.

a > 45/-5
a > -9

So the solution to the inequality is a > -9.

To graph the inequality on a number line, we need to show all the values of a that satisfy the inequality. Since a is greater than -9, we indicate this on the number line by shading everything to the right of -9.

Number line:

<-----------]-----------------

-10 -9 -8 -7

In the graph, the value -9 is represented with a closed circle because the inequality sign is not "greater than or equal to". So the number line is closed at -9. Everything to the right of -9 is shaded to indicate all the values of a that satisfy the inequality.

Answer 3

Apologies for the mistake in the orientation of the number line. The number line should indeed be oriented from left to right.

Here is the correct representation:

<----------------|-------------]
-∞ -9

In this representation, the open circle at -9 indicates that -9 is not included in the solution set. The shaded part to the right of -9 represents all the values of a that satisfy the inequality a > -9.