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Solve the inequality and graph the solution. 10>12–q
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GPT 3.5
To solve the inequality 10 > 12 - q, we can start by subtracting 12 from both sides:
10 - 12 > 12 - q - 12
-2 > -q
Next, we can multiply both sides by -1 to change the direction of the inequality:
-2(-1) < -q(-1)
2 < q
So, the solution to the inequality is q > 2.
To graph the solution, we can represent the solution on a number line. We place an open circle on 2 to indicate that it is not included in the solution set, and shade to the right to show that q can take any value greater than 2.
On the number line, it will look like this:
---------------------------------------->
-4 -3 -2 -1 0 1 2 3 4
The shaded region will be on the right side of the open circle at 2.
10 - 12 > 12 - q - 12
-2 > -q
Next, we can multiply both sides by -1 to change the direction of the inequality:
-2(-1) < -q(-1)
2 < q
So, the solution to the inequality is q > 2.
To graph the solution, we can represent the solution on a number line. We place an open circle on 2 to indicate that it is not included in the solution set, and shade to the right to show that q can take any value greater than 2.
On the number line, it will look like this:
---------------------------------------->
-4 -3 -2 -1 0 1 2 3 4
The shaded region will be on the right side of the open circle at 2.
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