Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Algebra ↓


Linear Equations in One Variable


Linear equations in one variable are one of the fundamental concepts of algebra. Let's learn what these equations are, how they can be solved, and how they apply to real-life situations.

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the following form:

ax + b = 0

In this equation:

  • x is the variable.
  • a and b are constants.
  • The exponent of x is 1, which makes this a linear equation.

Examples of linear equations in one variable

Linear equations can take different forms, but they all represent a straight line when plotted on a graph. Here are some examples:

1. 2x + 3 = 7 2. -5x = 10 3. x/2 - 5 = 0

Solving linear equations in one variable

Solving a linear equation means finding the value of the variable that makes the equation true. Let's look at the steps to solve these equations.

General steps of the solution:

  1. Simplify both sides of the equation separately by distributing and combining like terms.
  2. Move all terms belonging to the variable to one side of the equation.
  3. Move all constant terms to the opposite side of the equation.
  4. Isolate the variables by dividing or multiplying them to get the solution.

Example 1: Solving 2x + 3 = 7

Follow the following steps to solve the equation:

Step 1: Subtract 3 from both sides 2x + 3 - 3 = 7 - 3 2x = 4 Step 2: Divide both sides by 2 2x/2 = 4/2 x = 2

Thus, the solution for x is 2.

Example 2: Solving -5x = 10

Step 1: Divide both sides by -5 -5x/-5 = 10/-5 x = -2

The solution of this equation is x = -2.

Example 3: Solving x/2 - 5 = 0

Step 1: Add 5 to both sides x/2 - 5 + 5 = 0 + 5 x/2 = 5 Step 2: Multiply both sides by 2 2 * (x/2) = 5 * 2 x = 10

This gives the solution x = 10.

Viewing linear equations in one variable

Visualization makes linear equations easier to understand. Consider the equation 2x + 3 = 7:

x=2

Here, you can see the intersection of the line 2x + 3 = 7 with the x-axis, where x equals 2. This point represents the solution graphically.

Applications of linear equations in real life

Linear equations are not just theoretical concepts but have a variety of practical applications, including:

  • Financial planning: Budgeting income and expenses often involves solving equations.
  • Construction: Calculating length, width and cost of materials using linear equations.
  • Science: Formulas relating to speed, distance, and time can often be represented by linear equations.

Example: Budget planning

Suppose you earn $5000 per month and plan to save some amount every month. After setting aside your savings and paying all expenses, you are left with $1500. If we assume x savings, the equation is as follows:

5000 - x = 1500

Solve for savings x:

Step 1: Move expenses to the opposite side -x = 1500 - 5000 -x = -3500 Step 2: Multiply by -1 to isolate xx = 3500

So, the savings is $3500.

Conclusion

Linear equations in one variable are important for developing problem-solving skills in mathematics. They are applicable in many areas of life, providing efficient methods for solving quantitative problems.

By understanding the basic structure and solving techniques, equations become less abstract and more practical tools for tackling everyday challenges. Continue practicing with different examples, visualizations, and real-life scenarios to achieve mastery.

Practice problems

Try solving these yourself:

  1. Solve the equation: 3x - 4 = 11
  2. Solve the equation: 4x + 2 = 10
  3. Solve the equation: -x/3 = 5
  4. If you spend $200 on groceries and save $100 out of your $1000 income, write down and solve the equation for your expenses.

Grade 8 → 2.4


U
username
0%
completed in Grade 8

← Prev (2.3.4)
Special Products
Next (2.4.1) →
Solving Linear Equations

Comments 



Linear Equations in One Variable

https://www.buddymath.com/g8/2.4?bmal=en