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Math  /  Algebra

Question2≥x+9 or 20<x+92 \geq x+9 \text { or } 20<x+9
Answer Attempt 1 out of 2 □\square □\square □\square □\square □\square
Inequality Notation: □\square Number Line:

Studdy Solution

STEP 1

1. We are given a compound inequality with the word "or," which means we need to find the union of the solution sets of each inequality.
2. We will solve each inequality separately and then combine the solutions.

STEP 2

1. Solve the inequality 2≥x+92 \geq x + 9.
2. Solve the inequality 20<x+920 < x + 9.
3. Combine the solutions using the "or" condition.
4. Express the solution in inequality notation.
5. Represent the solution on a number line.

STEP 3

Solve the inequality 2≥x+92 \geq x + 9:
Subtract 9 from both sides to isolate xx:
2−9≥x 2 - 9 \geq x
−7≥x -7 \geq x
This can also be written as:
x≤−7 x \leq -7

STEP 4

Solve the inequality 20<x+920 < x + 9:
Subtract 9 from both sides to isolate xx:
20−9<x 20 - 9 < x
11<x 11 < x
This can also be written as:
x>11 x > 11

STEP 5

Combine the solutions using the "or" condition:
The solutions are x≤−7 x \leq -7 or x>11 x > 11 .

STEP 6

Express the solution in inequality notation:
The solution is:
x≤−7orx>11 x \leq -7 \quad \text{or} \quad x > 11

STEP 7

Represent the solution on a number line:
- Draw a number line. - Shade the region to the left of −7-7 and include a closed circle at −7-7 to indicate that −7-7 is included in the solution. - Shade the region to the right of 1111 and use an open circle at 1111 to indicate that 1111 is not included in the solution.
The solution in inequality notation is x≤−7 x \leq -7 or x>11 x > 11 .

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