Solve for xx and graph the solution on the number line below.2, is less than, minus, 2, x, plus, 6, or, minus, 18, is greater than, minus, 2, x, plus, 62<−2x+6or−18>−2x+6
Question
Solve for xx and graph the solution on the number line below.2, is less than, minus, 2, x, plus, 6, or, minus, 18, is greater than, minus, 2, x, plus, 62<−2x+6or−18>−2x+6
Solution
The given inequalities are:
2 < -2x + 6 and -18 > -2x + 6
Let's solve each inequality separately.
- 2 < -2x + 6
Subtract 6 from both sides:
2 - 6 < -2x -4 < -2x
Divide both sides by -2 (remember to flip the inequality sign when dividing by a negative number):
-4 / -2 > x 2 > x or x < 2
- -18 > -2x + 6
Subtract 6 from both sides:
-18 - 6 > -2x -24 > -2x
Divide both sides by -2 (remember to flip the inequality sign when dividing by a negative number):
-24 / -2 < x 12 < x or x > 12
So, the solution to the inequalities is x < 2 or x > 12.
On the number line, this would be represented by an open circle at 2 and everything to the left of it, and an open circle at 12 and everything to the right of it.
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