Notice the graph has an open circle and is shaded to the right.
This means that any number to the right of (but not including) −16 will make this inequality true.

How do you know if this is correct?

Try one! How about −7?
Substitute -7 for x and check to see if it makes a true statement.
x + 6 > −10
−7 + 6 > −10 ?
−1 > −10
This is true!

What would happen if you picked a number not in the shaded region? Try −18.
x + 6 > −10
−18 + 6 > −10 ?
−12 > −10

Is −12 greater than −10? NO!

This is not a true statement. You can see that numbers in the non-shaded region are not solutions to the inequality.

This graph has a solid circle and is shaded to the right.  This means any number to the right of (and including) −4 will make this inequality true!

What if you had forgotten to flip the symbol? Would it really affect the answer?

In this case the final inequality would have been x ≤ –4. Let’s see if numbers less than -4 will make this inequality true.
Try x = –6
–3x + 11 ≤ 23
–3(–6) + 11 ≤ 23
18 + 11 ≤ 23
29 ≤ 23

Is 29 less than or equal to 23?

No, 29 is greater than 23. This goes to show that it does matter whether the sign is flipped when multiplying or dividing both sides by a negative number!

Therefore, any number to the left of –3 will make this inequality true.

A garment store takes orders for printing company logos on T-shirts. The store charges a fixed handling charge of $55 and an additional charge of $2.40 to print each T-shirt. The store offers a discount of 10% on the printing fee alone if an order contains more than 200 T-shirts. The equations above can be used to determine the total cost in dollars, C, to print x number of T-shirts.

We are given two equations above. The first equation relates to 200 or fewer T-shirts, and the second equation relates to more than 200 t-shirts.

We need to find the total cost, C, to print 300 t-shirts.

Because 300 is greater than 200, we must use the second equation.

C = 55 + 2.40x - 0.24x Because x = 300, replace x with 300.

C = 55 + 2.40(300) - 0.24(300) Simplify.

C = 55 + 720 – 72

C = 703

Check your answer.

C = 55 + 2.40(300) - 0.24(300) Replace C with 703.

703 = 55 + 720 – 72

703 = 703

Therefore, the total cost for printing 300 t-shirts is $703.00.