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SATISFY AN EQUATION INEQUALITY

Satisfy An Equation (Inequality)

Definition Of Satisfy An Equation (Inequality)

If the given value of a variable evaluates the equation or inequality to zero, then we say that the value satisfies the given equation or inequality.

Example of Satisfy an Equation (Inequality)

x + 12 - 25 = 0, For this equation, only x = 13 satisfies the equation as 13 + 12 - 25 = 0.
x + 3 < 9;="" in="" this="" inequality,="" x="" takes="" all="" the="" values="" less="" than="" 6="" as="" 6="" +="" 3="">

Video Examples: Equations and Inequalities

 

 

Solved Example on Satisfy an Equation (Inequality)

Ques: Identify the values that satisfy the equation. x - 24 = 0

Choices:

A. 0
B. 1
C. - 24
D. 24
Correct Answer: D

Solution:

Step 1: x - 24 = 0 [Original equation.] 
Step 2: 0 - 24 = 0 [Substitute x = 0 in the equation.] 
Step 3: - 24 = 0, which is not true
Step 4: So, 0 does not satisfy the given equation. 
Step 5: 1 - 24 = 0 [Substitute x = 1 in the equation.]
Step 6: - 23 = 0, which is not true 
Step 7: So, 1 does not satisfy the given equation. 
Step 8: - 24 - 24 = 0 [Substitute x = - 24 in the equation.]
Step 9: - 48 = 0, which is not true 
Step 10: So, - 24 do not satisfy the given equation. 
Step 11: 24 - 24 = 0 [Substitute x = 24 in the equation.]
Step 12: 0 = 0, which is true 
Step 13: So, x = 24 satisfy the given equation.

Quick Summary

  • A value satisfies an equation if substituting it results in a true statement (e.g., 0 = 0).
  • A value satisfies an inequality if substituting it results in a true inequality (e.g., 3 < 9).
\[ N/A (Concept is definitional rather than formula-based) \]

🍎 Teacher Insights

Emphasize the importance of showing the substitution steps clearly. Use visual aids like number lines to represent the solutions of inequalities. Provide varied examples, including equations and inequalities with different levels of complexity.

🎓 Prerequisites

  • Basic arithmetic operations
  • Understanding of variables
  • Concept of equality and inequality

Check Your Knowledge

Q1: Which value satisfies the equation x - 5 = 0?

Q2: Which value satisfies the inequality x + 2 < 7?

Q3: Does x = -3 satisfy the equation 2x + 6 = 0?

Frequently Asked Questions

Q: How do I check if a value satisfies an equation?
A: Substitute the value for the variable in the equation and simplify. If the resulting statement is true, the value satisfies the equation.

Q: Can an equation have more than one solution that satisfies it?
A: Yes, depending on the equation. Some equations have one solution, some have multiple, and some have infinitely many.

Q: Can an inequality have more than one solution that satisfies it?
A: Yes, inequalities typically have a range of solutions.

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