Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (\varnothing∅), leave the number line blank.13, is less than or equal to, minus, 5, x, plus, 3, or, minus, 47, is greater than or equal to, minus, 5, x, plus, 313≤−5x+3or−47≥−5x+3
Question
Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (\varnothing∅), leave the number line blank.13, is less than or equal to, minus, 5, x, plus, 3, or, minus, 47, is greater than or equal to, minus, 5, x, plus, 313≤−5x+3or−47≥−5x+3
Solution
The given inequalities are:
- 13 ≤ -5x + 3
- -47 ≥ -5x + 3
Let's solve each inequality step by step:
-
13 ≤ -5x + 3 Subtract 3 from both sides to isolate the term with x: 10 ≤ -5x Divide both sides by -5 (remember to flip the inequality sign when dividing by a negative number): -2 ≥ x or x ≤ -2
-
-47 ≥ -5x + 3 Subtract 3 from both sides: -50 ≥ -5x Divide both sides by -5 (again, remember to flip the inequality sign): 10 ≤ x or x ≥ 10
So, the solution to the inequalities is x ≤ -2 or x ≥ 10.
On the number line, this would be represented by a closed circle at -2 and all points to the left of it, and a closed circle at 10 and all points to the right of it.
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