Simple Equations: A Complete Guide for Class 7

What Exactly is a Simple Equation?

Think of a weighing scale. If you put 5 kg on the left side, you must put 5 kg on the right side for it to be balanced. An equation works the same way! It's a statement that says two things are equal. It has an equals sign (=) in the middle.

The part on the left of the equals sign is called the Left Hand Side (LHS), and the part on the right is called the Right Hand Side (RHS).

An equation also contains a variable, which is a letter (like x, y, p, m) that represents an unknown number we need to find. It also has constants, which are just the fixed numbers we know. For example, in the equation x + 3 = 8, 'x' is the variable, 3 and 8 are constants, 'x + 3' is the LHS, and '8' is the RHS. The whole statement is an equation. A 'simple equation' is one where the variable has a power of 1 (you won't see x² or x³).

Turning Words into Maths: Setting up Equations

The sum of a number and 5 is 12.

Let the number be 'x'. The equation is: x + 5 = 12

7 subtracted from a number gives 3.

Let the number be 'y'. The equation is: y - 7 = 3

Four times a number is 20.

Let the number be 'p'. The equation is: 4p = 20

A number divided by 2, plus 1, gives 9.

Let the number be 'm'. The equation is: (m/2) + 1 = 9

Finding the Solution: The Balancing Method

1. Step 1: Understand the Goal - Isolate the Variable — Our main mission is to get the variable (like 'x') all by itself on one side of the equals sign. This will tell us its value.
2. Step 2: The Golden Rule - Do the Same to Both Sides — To keep the equation's 'scale' balanced, whatever operation you do to one side (LHS), you MUST do the exact same thing to the other side (RHS). We use inverse (opposite) operations to cancel out numbers. Addition is the inverse of Subtraction, and Multiplication is the inverse of Division.
3. Step 3: A Worked Example: Solve x + 4 = 10 — To get 'x' alone, we need to remove the '+4'. The opposite of adding 4 is subtracting 4. So, we subtract 4 from BOTH sides: (x + 4) - 4 = 10 - 4 On the LHS, +4 and -4 cancel out, leaving just 'x'. On the RHS, 10 - 4 = 6. So, x = 6.
4. Step 4: Check Your Answer - Verification is Key! — Always check your work! Put the solution back into the original equation. If x = 6, our equation was x + 4 = 10. Let's substitute: 6 + 4 = 10. Since 10 = 10, our LHS equals our RHS, and the answer is correct! Hooray!

Exam Tips: Avoid These Common Mistakes!

Solving equations is easy once you know the rules, but watch out for these traps!

1. Forgetting the Golden Rule: A very common error is to subtract a number from the LHS but forget to subtract it from the RHS. Remember, the equation must always be balanced!
2. Sign Errors with Transposing: When you move a term from one side to the other (transposing), you must change its sign. A +5 on the LHS becomes a -5 on the RHS. A ×3 on the LHS becomes a ÷3 on the RHS. Forgetting to flip the sign or operation is a major source of wrong answers.
3. Incorrect Order of Operations: When solving an equation like 2x + 5 = 15, deal with the addition/subtraction first. Get rid of the +5 before you deal with the 2x. The correct first step is to subtract 5 from both sides.

Practice Questions with Solutions

• Q: Solve: 3n - 2 = 13 A: Step 1: To isolate the term with 'n', we need to remove '-2'. We do this by adding 2 to both sides of the equation. 3n - 2 + 2 = 13 + 2 3n = 15 Step 2: Now, to get 'n' by itself, we need to undo the multiplication by 3. We do this by dividing both sides by 3. 3n / 3 = 15 / 3 n = 5 Final answer: n = 5
• Q: The sum of three times a number and 11 is 32. Find the number. A: Step 1: First, let's write this statement as an equation. Let the number be 'x'. 'Three times a number' is 3x. 'The sum of 3x and 11' is 3x + 11. The equation is: 3x + 11 = 32 Step 2: Solve the equation. Subtract 11 from both sides. 3x + 11 - 11 = 32 - 11 3x = 21 Step 3: Divide both sides by 3. 3x / 3 = 21 / 3 x = 7 Final answer: The number is 7.
• Q: Solve: y/5 + 3 = 7 A: Step 1: First, isolate the term with 'y' by subtracting 3 from both sides. (y/5) + 3 - 3 = 7 - 3 y/5 = 4 Step 2: To get 'y' by itself, we need to undo the division by 5. We do this by multiplying both sides by 5. (y/5) 5 = 4 5 y = 20 Final answer: y = 20
• Q: Raju's father's age is 5 years more than three times Raju's age. Find Raju's age, if his father is 44 years old. A: Step 1: Let Raju's age be 'r'. 'Three times Raju's age' is 3r. '5 years more than 3r' is 3r + 5. This is equal to his father's age, which is 44. So the equation is: 3r + 5 = 44 Step 2: Solve for 'r'. Subtract 5 from both sides. 3r + 5 - 5 = 44 - 5 3r = 39 Step 3: Divide both sides by 3. 3r / 3 = 39 / 3 r = 13 Final answer: Raju's age is 13 years.

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