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QuestionSolve the inequality 3x−5−3>5\frac{3 x-5}{-3}>5 and provide the solution set in interval and graph forms.

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality 3x−5−3>5\frac{3x -5}{-3} >5. . The solution set is a range of values for xx that satisfy the inequality.

STEP 2

First, we need to isolate the xx term. We can do this by multiplying both sides of the inequality by −-. Remember that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.
x−5<−×5x -5 < - \times5

STEP 3

Now, simplify the right side of the inequality.
3x−5<−153x -5 < -15

STEP 4

Next, we want to isolate xx by itself on one side of the inequality. We can do this by adding $$ to both sides of the inequality.
3x<−15+3x < -15 +

STEP 5

implify the right side of the inequality.
3x<−103x < -10

STEP 6

Finally, divide both sides of the inequality by 33 to solve for xx.
x<−103x < \frac{-10}{3}

STEP 7

So, the solution to the inequality in interval notation is (−∞,−103)(-\infty, -\frac{10}{3}).

STEP 8

To graph the solution set, we draw a number line. We put a open circle at −103-\frac{10}{3} (because the inequality is strictly less than, not less than or equal to) and shade everything to the left of −103-\frac{10}{3}, indicating that all those values are part of the solution set.
The solution set is option A. The solution set is (−∞,−103)(-\infty, -\frac{10}{3}).

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