Convert to Interval Notation |5-2x|>3

Problem

|5−2*x|>3

Solution

1. Identify the type of inequality. Since the absolute value is greater than a positive number, the expression inside the absolute value must be either greater than the positive value or less than its negative.

2. Set up two separate linear inequalities based on the absolute value property |u|>a⇒u>a* or *u<−a

5−2*x>3

5−2*x<−3

3. Solve the first inequality by subtracting 5 from both sides.

−2*x>−2

4. Divide by −2 and reverse the inequality sign.

x<1

5. Solve the second inequality by subtracting 5 from both sides.

−2*x<−8

6. Divide by −2 and reverse the inequality sign.

x>4

7. Combine the solutions using the union symbol to express the solution in interval notation.

(−∞,1)∪(4,∞)

Final Answer

|5−2*x|>3=(−∞,1)∪(4,∞)

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