Math Problem Statement

2𝑥−7<4𝑥−2

Solution

To solve the inequality:

2x7<4x22x - 7 < 4x - 2

  1. First, bring all terms involving xx to one side of the inequality. Subtract 2x2x from both sides:

    7<2x2-7 < 2x - 2

  2. Next, add 22 to both sides to isolate the term with xx:

    5<2x-5 < 2x

  3. Finally, divide both sides by 22 to solve for xx:

    x>52x > -\frac{5}{2}

So, the solution is:

x>52x > -\frac{5}{2}

Would you like more details on any step or have any questions?

Related Questions

  1. How would you solve 3x4<2x+13x - 4 < 2x + 1?
  2. How can inequalities change if you multiply or divide by a negative number?
  3. What is the solution to 5x+3>2x+95x + 3 > 2x + 9?
  4. How would you solve a compound inequality like 2x+3<52x + 3 < 5 and 3x1>23x - 1 > 2?
  5. Can you graph x>52x > -\frac{5}{2} on a number line?

Tip

When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Properties of inequalities when adding/subtracting terms
Properties of inequalities when dividing/multiplying both sides by a constant

Theorems

Properties of inequalities

Suitable Grade Level

Grades 8-10