Solve the Inequality by following the steps: 2x / x+1 ≥ 1 Step 1. Put the rational inequality in the general form where > can be replaced by <, ≤ and ≥. R(x)/Q(x) > 0 Step 2. Write the inequality into a single rational expression on the left-hand side. Note: Remember that one side must always be zero and the other side is always a single fraction, so simplify the fractions if there is more than one fraction. Step 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. Step 4. Plot the critical values on a number line, breaking the number line into intervals. Step 5. Substitute critical values to the inequality to determine if the endpoints of the intervals in the Solution should be included or not. Step 6. Select test values in each interval and substitute those values into the inequality. Note: a. If the test value makes the inequality TRUE, then the entire interval is a solution to the inequality. b. If the test value makes the inequality FALSE, then the entire interval is not a solution to the inequality. Step 7. Use interval notation to write the final answer.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve the Inequality by following the steps:

2x / x+1 ≥ 1

Step 1. Put the rational inequality in the general form where > can be replaced by <, ≤ and ≥.

R(x)/Q(x) > 0

Step 2. Write the inequality into a single rational expression on the left-hand side.

Note: Remember that one side must always be zero and the other side is always a single fraction, so simplify the fractions if there is more than one fraction.

Step 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values.

Step 4. Plot the critical values on a number line, breaking the number line into intervals.

Step 5. Substitute critical values to the inequality to determine if the endpoints of the intervals in the Solution should be included or not.

Step 6. Select test values in each interval and substitute those values into the inequality.

Note:

a. If the test value makes the inequality TRUE, then the entire interval is a solution to the inequality.

b. If the test value makes the inequality FALSE, then the entire interval is not a solution to the inequality.

Step 7. Use interval notation to write the final answer.

2x
> 1
X+1
Transcribed Image Text:2x > 1 X+1
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