Math

QuestionSolve the inequality 53x39x5 - 3x \leq 3 - 9x and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. We are given a linear inequality 53x39x5-3x \leq3-9x. . We need to solve this inequality for xx.
3. The solution should be expressed in interval notation.

STEP 2

First, we need to isolate the xx terms on one side of the inequality. We can do this by adding 9x9x to both sides of the inequality.
5x+9x9x+9x5-x +9x \leq-9x +9x

STEP 3

implify the inequality by performing the addition on both sides.
5+6x35 +6x \leq3

STEP 4

Next, we need to isolate xx on one side of the inequality. We can do this by subtracting $$ from both sides of the inequality.
+6x3 +6x - \leq3 -

STEP 5

implify the inequality by performing the subtraction on both sides.
x2x \leq -2

STEP 6

Finally, to isolate xx, we divide both sides of the inequality by 66.
6x626\frac{6x}{6} \leq \frac{-2}{6}

STEP 7

implify the inequality to get the solution for xx.
x13x \leq -\frac{1}{3}

STEP 8

Express the solution in interval notation. Since xx is less than or equal to 13-\frac{1}{3}, the interval notation is (,13](-\infty, -\frac{1}{3}].
The solution to the inequality 53x3x5-3x \leq3-x is x13x \leq -\frac{1}{3}, or in interval notation, (,13](-\infty, -\frac{1}{3}].

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