How do you solve and graph # 2(q - 3) + 6 ≤ -10#?

Answer 1

Eva Adamson

#q < -5#

#2(q-3) + 6 <= -10#

Distribute the left side:
#2q - 6 + 6 <= -10#

Simplify the left side:
#2q <= -10#

Divide both sides by #color(blue)2#:
#(2q)/color(blue)2 <= (-10)/color(blue)2#

#q < -5#

Here's a graph of it on a number line:

The open circle on #-5# means that #-5# is not a solution (but anything less than it is).

Hope this helps!

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Answer 2

Avery Alexander

To solve and graph the inequality 2(q - 3) + 6 ≤ -10, follow these steps:

First, simplify the inequality: 2(q - 3) + 6 ≤ -10 2q - 6 + 6 ≤ -10 2q ≤ -10
Next, isolate q: 2q ≤ -10 q ≤ -5
Now, graph the solution on a number line. Since q ≤ -5, you will shade the region to the left of -5, including -5.

This represents the solution to the inequality 2(q - 3) + 6 ≤ -10.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.