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 Two-Step Equations


In algebra, you will often come across equations that require more than one step to solve. These are known as two-step equations. This means that you have to perform two operations to find the value of the variable. Let's take a deeper look at how to solve two-step equations in a simple and easy to understand way.

Understanding the basics

Before we begin solving two-step equations, let's first remember what an equation is. An equation is a mathematical statement that shows that two expressions are equal. It often includes a variable, such as x or y, which represents an unknown number you need to find.

A basic equation looks like this:

x + 5 = 12

Here, x is our variable, and we need to find the value of x that makes both sides of the equation equal. This example is a one-step equation because you can solve it by performing a single operation: subtracting 5 from both sides.

In contrast, a two-step equation might look like this:

2x + 3 = 11

Here, you need to perform two operations to isolate x and find its value.

Steps to solve two-step equations

Let's understand the process of solving a two-step equation. We will follow these general steps:

  1. Identify operations that affect the variable. Identify combined operations with variables on the same side of the equation.
  2. Undo the addition or subtraction. Use the inverse operation to remove the constant term on the variable side.
  3. Undo the multiplication or division. Use the inverse operation to solve for the variable.

Let's use these steps to solve our example equation:

Example 1: Solving 2x + 3 = 11

Step 1: Identify the operations affecting x

In 2x + 3 = 11, the variable x is being multiplied by 2, and then 3 is being added. We will reverse these operations.

Step 2: Undo the addition

Subtract 3 from both sides of the equation to remove +3:

2x + 3 - 3 = 11 - 3

The simplification of which is as follows:

2x = 8

Step 3: Undo the multiplication

To solve for x, divide both sides by 2:

2x / 2 = 8 / 2

From this we get:

x = 4

So, the solution of the equation 2x + 3 = 11 is x = 4.

Let’s look at another example!

For better understanding consider the equation:

3x - 4 = 5
3x – 4 = 5

Step 1: Identify the operations affecting x

The variable x is multiplied by 3, and 4 is subtracted. We will reverse these operations.

Step 2: Undo the subtraction

Add 4 to both sides to cancel the subtraction:

3x - 4 + 4 = 5 + 4

The simplification of which is as follows:

3x = 9

Step 3: Undo the multiplication

Divide both sides by 3:

3x / 3 = 9 / 3

From this we get:

x = 3

Therefore, the solution of the equation 3x - 4 = 5 is x = 3.

More practice problems

Let's practice solving two-step equations using the steps we just learned. This will strengthen your understanding.

Example 2: 5x + 7 = 22

Step 1: Identify the operations affecting x.

In 5x + 7 = 22, x is multiplied by 5, and then 7 is added.

Step 2: Undo the sum by subtracting 7 from both sides:

5x + 7 - 7 = 22 - 7

Simplification:

5x = 15

Step 3: Undo the multiplication by dividing both sides by 5:

5x / 5 = 15 / 5

which gives:

x = 3

Example 3: 4x - 10 = 6

Step 1: Identify the operations affecting x.

Here, x is multiplied by 4, and 10 is subtracted.

Step 2: Undo the subtraction by adding 10 to both sides:

4x - 10 + 10 = 6 + 10

Simplification:

4x = 16

Step 3: Undo the multiplication by dividing both sides by 4:

4x / 4 = 16 / 4

this results in:

x = 4

Key points to remember

  • Always do the opposite operation to isolate the variable.
  • Balance the equation by performing the same operation on both sides.
  • Check your solution by substituting it back into the original equation to make sure it makes both sides equal.

Conclusion

Solving two-step equations is a foundational skill in algebra that develops logical thinking and problem-solving abilities. By mastering the process of identifying operations and applying inverse operations step-by-step, you can solve these equations with confidence. Remember, constant practice is key to understanding and becoming proficient at two-step equations. Keep practicing different problems to further enhance your skills!


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Solving Two-Step Equations

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