Convert to Interval Notation 1/2x-2/3>2

Problem

1/2*x−2/3>2

Solution

1. Add 2/3 to both sides of the inequality to isolate the term containing x

1/2*x>2+2/3

2. Find a common denominator to combine the constants on the right side.

1/2*x>6/3+2/3

1/2*x>8/3

3. Multiply both sides by 2 to solve for x

x>8/3⋅2

x>16/3

4. Convert the inequality to interval notation. Since x is strictly greater than 16/3 use a parenthesis at 16/3 and extend to infinity.

(16/3,∞)

Final Answer

1/2*x−2/3>2⇒(16/3,∞)

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