EQUATION

Equation

Definition Of Equation

An Equation is a mathematical sentence that uses the equal sign (=) to show that two expressions are equal.

Example of Equation

The following are some examples of equation.
10 + 2 = 12
4a - 3b = 1
e^x + y = - 2

Video Examples:Solving Linear Equations

Solved Example on Equation

Ques: Solve the equation for x: 7x + 8 = 1

Choices:

A. 1
B. 9/7
C. - 1
D. 8/7
Correct Answer: C

Solution:

Step 1: 7x + 8 = 1
Step 2: Subtracting 8 from each side, we get, 7x = - 7.
Step 3: Dividing both sides by - 7, we get, x = - 1.

Quick Summary

An equation uses an equal sign (=).
Equations show that two expressions have the same value.

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⚠️ Common Mistakes

Incorrectly applying operations to only one side of the equation.
Forgetting to simplify expressions before solving.

🌍 Real-World Uses

Balancing a budget: Ensuring that income equals expenses.
Calculating the trajectory of a projectile: Solving equations of motion to determine where a ball will land.
Mixing chemical solutions: Determining the precise amount of each substance needed to achieve a desired concentration by solving a system of equations.

📋 Standards Alignment

CCSS.MATH.CONTENT.6.EE.B.5
CCSS.MATH.CONTENT.7.EE.B.4

🍎 Teacher Insights

Emphasize the importance of performing the same operation on both sides of the equation to maintain balance. Use visual aids like scales to demonstrate this concept.

🎓 Prerequisites

Basic Arithmetic
Understanding of Variables

Check Your Knowledge

Q1: Solve for x: x + 5 = 10

A. 5 B. 10 C. 15 D. 2

Frequently Asked Questions

Q: What is the difference between an equation and an expression?
A: An equation contains an equals sign, indicating equality. An expression is a combination of terms without an equals sign.