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QuestionSolve the inequality 3x+2≤−103x + 2 \leq -10 and graph the solution on the number line provided.

Studdy Solution

STEP 1

Assumptions1. The inequality is 3x+≤−103x + \leq -10 . We are solving for xx

STEP 2

First, we need to isolate xx in the inequality. We can do this by subtracting 22 from both sides of the inequality.
x+2−2≤−10−2x +2 -2 \leq -10 -2

STEP 3

implify the inequality.
3x≤−123x \leq -12

STEP 4

Next, divide both sides of the inequality by 33 to solve for xx.
3x3≤−123\frac{3x}{3} \leq \frac{-12}{3}

STEP 5

implify the inequality to get the solution.
x≤−4x \leq -4

STEP 6

Now, we need to graph the solution on a number line. Draw a number line and mark the point −4-4 on it.

STEP 7

Since the inequality is x≤−4x \leq -4, this means that xx can be −4-4 or any number less than −4-4. So, the graph should include the point −4-4 and all points to the left of −4-4.
To represent this on the number line, draw a closed circle at −4-4 and draw a line extending to the left from −4-4.
The solution to the inequality 3x+2≤−103x +2 \leq -10 is x≤−4x \leq -4.

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