Math Problem Statement

Solve for x and graph the solution on the number line: 4 < x - 1

Solution

The question visible in your image asks you to solve the inequality 4<x14 < x - 1 and graph the solution on the number line.

Step 1: Solve the inequality

Given: 4<x14 < x - 1 To isolate xx, add 1 to both sides: 4+1<x4 + 1 < x 5<x5 < x Or equivalently: x>5x > 5

Step 2: Inequality Notation

The solution in inequality notation is: x>5x > 5

Step 3: Graphing on the number line

On the number line, you would represent this by:

  • An open circle at x=5x = 5 (since xx is strictly greater than 5, not equal to 5).
  • A line extending to the right, indicating all values greater than 5.

Once you've represented this on the number line and input the inequality notation, you can submit your answer.

Do you have any questions or would you like further details on this problem?

Here are 5 related questions:

  1. What is the difference between a strict inequality and a non-strict inequality?
  2. How do you graph inequalities that involve "less than or equal to"?
  3. What are compound inequalities and how are they solved?
  4. Can an inequality have no solution? If yes, how can you recognize this?
  5. What changes when solving an inequality involving negative values?

Tip: When solving inequalities, always remember that multiplying or dividing by a negative number flips the inequality sign.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Number Line Graphing

Formulas

Basic inequality manipulation
x > b (after isolating x)

Theorems

Properties of inequalities
Transitive property

Suitable Grade Level

Grade 7