Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Algebra → Linear Equations ↓


Solving Simple Equations


Linear equations are mathematical statements of equality involving constants and variables. In grade 7 math, solving simple linear equations involves finding the value of the variable that makes the equation true. We will explore this concept using text explanations, examples, and visual illustrations.

Understanding linear equations

A simple linear equation in algebra is usually written in the form:

ax + b = c

In this form:

  • a, b and c are constants (known numbers).
  • x is the variable (the unknown number we need to find).

Our goal when solving these equations is to determine the value of the variable (x) by isolating it on one side of the equation.

Basic steps to solve simple equations

Simple steps can be followed to solve simple linear equations. Let us see these steps used to solve the equation step by step.

Example 1: Solving x + 5 = 12

Step 1: Identify what is on both sides of the equation. Our equation is:

x + 5 = 12

Step 2: The goal is to get x alone on one side of the equation. We do this by cancelling out the constant on the side with the variable. Here, we need to remove +5.

Step 3: Use the inverse operation. The inverse of addition is subtraction. So, subtract 5 from both sides.

(x + 5) - 5 = 12 - 5

By simplification we get:

x = 7

This means that when x is 7, the equation x + 5 = 12 is true. We can check this by substituting 7 back into the equation:

7 + 5 = 12

So, 12 = 12, which confirms that our solution is correct.

Example 2: Visual example of solving 2x = 10

2x 10

The rectangles given above have 2x written on one side and 10 on the other. To solve 2x = 10, we have to find the value of x.

Step 1: Divide both sides by 2 (the inverse of multiplying by 2).

(2x)/2 = 10/2

Step 2: Simplify both sides:

x = 5

Therefore, the solution of the equation is x = 5.

More text examples with step-by-step explanations

Example 3: Solving 3x - 4 = 11

This equation involves subtraction operation.

Step 1: Solve the subtraction problem by adding 4 to both sides of the equation.

3x - 4 + 4 = 11 + 4

This makes it simpler:

3x = 15

Step 2: Now, to isolate x, divide both sides by 3.

(3x)/3 = 15/3

By simplification we get:

x = 5

Check: Substitute 5 into the original equation:

3(5) - 4 = 11

Simplifying, 15 - 4 = 11, which is correct.

Example 4: Solving 4 + x = 20

Step 1: We need to isolate x by cancelling out the constant. Subtract 4 from both sides.

4 + x - 4 = 20 - 4

Simplifying both sides, we get:

x = 16

Check: Substitute 16 into the original equation:

4 + 16 = 20

Simplifying, 20 = 20, which is correct.

Summary

Solving simple equations involves a few essential steps: understanding the structure of the equation, performing inverse operations to isolate the variable, and then simplifying to find the value of the unknown. Practice is key to becoming proficient at solving equations, and visualizing the balance between the two sides can help understand the process.

Remember, the concept of balancing an equation is like a scale, where the goal is to keep both sides equal, while performing operations to isolate and determine the unknown variable.


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Linear Equations
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Solving Simple Equations

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