Question

Solve the inequality. Graph the solution set and write it in interval notation.

- 4 < 2(x - 2) <= 11

Write the answer in interval notation.
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(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Answer 1

To solve the inequality -4 < 2(x - 2) <= 11, we can simplify and solve each part separately.

Starting with 2(x - 2), we distribute the 2: 2(x - 2) = 2x - 4.

The inequality becomes:

-4 < 2x - 4 ≤ 11

Adding 4 to each part, we have:

0 < 2x ≤ 15

Dividing each part by 2, we get:

0 < x ≤ 7.5

So the solution set for the inequality is the interval (0, 7.5].

Graphically, this means that x is greater than 0 but less than or equal to 7.5, so the solution would be represented by a shaded line segment from 0 to 7.5, with 0 being an open circle and 7.5 being a closed circle.

The solution set in interval notation is: (0, 7.5]