step 1 We have to solve 4 is less than equal to 1 minus x less than equal to 6. First, subtract 1 from

Question

Solve. $$4 \leq 1-x \leq 6$$

Name: Problem 88, Chapter 5: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-20T04:27:26-08:00
Duration: 1 min 2 s
Channel: Ankit Gupta
Description: Solve. 4 ≤1-x ≤6

   Solve.
$$4 \leq 1-x \leq 6$$

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 5, Problem 88

Instant Answer

Solved by Expert Ankit Gupta

07/20/2020

Step 1

Step 1: First, we subtract 1 from all parts of the inequality: $$4-1 \leq 1-x-1 \leq 6-1$$ This simplifies to: $$3 \leq -x \leq 5$$ Show more…

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Solve. $$4 \leq 1-x \leq 6$$

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Key Concepts

Inequality Manipulation

Manipulating inequalities involves performing operations such as addition or subtraction on all parts of the inequality at once. This helps isolate the variable without altering the intrinsic order of the inequality, ensuring that the solution remains valid across the entire range.

Multiplying or Dividing by a Negative Number

When multiplying or dividing an inequality by a negative number, the direction of the inequality symbols must be reversed. This key property is essential in solving inequalities accurately, especially when the variable is being solved through operations that involve negative factors.

Compound Inequalities

Compound inequalities involve expressions where one variable is simultaneously bounded by two inequalities. They require applying operations across all parts of the inequality while maintaining the relationships, allowing for the determination of a solution set that satisfies both inequalities concurrently.

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