Math

QuestionSolve the inequality and express the solution set in interval notation: 2x+511-2x + 5 \leq 11.

Studdy Solution

STEP 1

Assumptions1. The inequality is x+511-x +5 \leq11 . We need to solve for xx
3. The solution should be presented in interval notation

STEP 2

First, we need to isolate xx on one side of the inequality. We can do this by subtracting 55 from both sides.
2x+55115-2x +5 -5 \leq11 -5

STEP 3

implify the inequality.
2x6-2x \leq6

STEP 4

To isolate xx, we divide both sides of the inequality by 2-2. Remember, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
2x262\frac{-2x}{-2} \geq \frac{6}{-2}

STEP 5

implify the inequality to find the solution.
x3x \geq -3

STEP 6

Now we need to represent this solution in interval notation. The solution x3x \geq -3 can be written in interval notation as [3,)[-3, \infty).
The solution to the inequality 2x+511-2x +5 \leq11 is x3x \geq -3 or in interval notation, [3,)[-3, \infty).

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