Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Algebra ↓


Solving Simple Equations


Solving simple equations is one of the basic skills in algebra. An equation is like a scale where both sides are equal. The goal is to find the value of an unknown variable, usually represented by a letter like x, that makes the equation true. Let's understand how to solve these equations step by step with clear examples.

What is the equation?

An equation is a mathematical statement that shows equality between two expressions. It has two sides: left side and right side. Here's what a simple equation looks like:

3 + x = 7

In this equation, 3 + x is the left side, and 7 is the right side. Our task is to find what value of x makes both sides equal.

Concept of balance scale

Think of the equation like a balance scale. Whatever you do on one side of the equation to maintain balance, you must do the same on the other side.

3 + x 7

If you add, subtract, multiply, or divide one side, you must do the same to the other side to keep it balanced.

Steps to solve simple equations

Step 1: Isolate the variables

The first step is to bring the unknown variable to one side of the equation. You can do this by performing operations that will cancel out the other numbers or variables around it.

Consider the equation:

3 + x = 7

To get x alone, you subtract 3 from both sides:

3 + x - 3 = 7 - 3

The simplification of which is as follows:

x = 4

Example 1

Let's solve the equation x - 5 = 10.

To get x alone, add 5 to both sides:

x - 5 + 5 = 10 + 5

so,

x = 15
X – 5 10

Step 2: Simplify each side

Make sure each side of your equation is as simple as possible. Sometimes, you may need to combine or distribute like terms.

For example:

2x + 3x = 10

Combine like terms 2x and 3x:

5x = 10

Now divide both sides by 5 to find the value of x:

5x / 5 = 10 / 5

like this,

x = 2

Example 2

Solve the equation 4(x - 1) = 12.

First, distribute 4:

4 * x - 4 * 1 = 12

The simplification of which is as follows:

4x - 4 = 12

Add 4 to both sides:

4x - 4 + 4 = 12 + 4

So it becomes:

4x = 16

Finally, divide both sides by 4:

x = 16 / 4

Due to this:

x = 4

Step 3: Check your solution

Always plug the values back into the original equation to make sure your solution is correct. For the equation 3 + x = 7, check if we get x = 4:

3 + 4 = 7

Since this statement is true, the solution is correct.

Example 3

Let's check our solution for the equation 2x + 3 = 9.

We get that x = 3 Substitute x = 3 back into the original equation:

2 * 3 + 3 = 9

Calculate:

6 + 3 = 9

Since this is true, our solution is verified.

Common mistakes and tips

When solving simple equations, avoid these common mistakes:

  • Not balancing both sides of an equation: Always perform the same operation on both sides.
  • Forgetting to simplify: Combine like terms and simplify each side whenever possible.
  • Skipping the verification step: Always substitute your solution into the original equation to check your work.

Practice problems

Try solving these equations yourself and check your answers:

  1. x + 6 = 15
  2. 2x - 8 = 0
  3. 3(x + 1) = 12
  4. 5x = 20
  5. 10 - x = 3

Solution:

  1. x = 9
  2. x = 4
  3. x = 3
  4. x = 4
  5. x = 7

Conclusion

Understanding how to solve simple equations is fundamental in algebra. Remember to always perform the same operation on both sides of the equation and check your solutions by substituting them back into the original equation. Practice regularly to become more familiar and comfortable solving different types of equations.


Grade 6 → 2.2


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Algebraic Terms and Coefficients
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Balancing Equations

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Solving Simple Equations

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