Math Problem Statement

1-4x>19 find x

Solution

To solve the inequality 14x>191 - 4x > 19:

  1. Subtract 1 from both sides to isolate the term involving xx: 14x1>1911 - 4x - 1 > 19 - 1 This simplifies to: 4x>18-4x > 18

  2. Divide both sides by -4. Since we are dividing by a negative number, reverse the inequality sign: x<184x < \frac{18}{-4} Simplifying the fraction: x<92orx<4.5x < -\frac{9}{2} \quad \text{or} \quad x < -4.5

Solution:

x<4.5x < -4.5

Would you like further details or have any questions?


Here are 5 related questions:

  1. What is the solution set for 23x72 - 3x \geq 7?
  2. Solve 5x92x+35x - 9 \leq 2x + 3.
  3. How do you solve 2x+8>4-2x + 8 > 4?
  4. What happens if you divide an inequality by a negative number?
  5. Solve the system of inequalities 3x243x - 2 \leq 4 and x+1>0x + 1 > 0.

Tip: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

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Math Problem Analysis

Mathematical Concepts

Inequalities
Linear Equations

Formulas

Basic inequality manipulation

Theorems

Rule of reversing inequality when dividing by a negative number

Suitable Grade Level

Grades 8-10