Simple Equations

An equation is a condition on a variable, stating that two expressions are equal. In 4x + 5 = 65, the expression 4x + 5 is the left hand side (LHS), 65 is the right hand side (RHS), and the value of the variable that makes LHS equal to RHS is the solution. Here x = 15 is the solution, because 4 x 15 + 5 = 65. An equation remains balanced, like a weighing scale, if we add, subtract, multiply or divide both sides by the same non-zero number. A quicker method is transposing: moving a term from one side to the other while changing its sign, so in 3p - 10 = 5 we get 3p = 15 and p = 5. You also learn to build equations from a given solution and to convert word statements into equations. The chapter ends with practical problems on ages, money, the perimeter of figures and the angles of a triangle, which are solved by framing a simple linear equation in one variable.

Detailed Worksheet: Simple Equations Section A - Definitions (10 marks) 1. What is an equation? How is it different from an expression? (2 marks) 2. What is meant by the solution of an equation? Check whether x = 3 is a solution of 5x + 2 = 17. (2 marks) 3. What is transposing? Explain with an example. (2 marks) 4. State the rules for keeping an equation balanced. (2 marks) 5. Identify the LHS and RHS of 3n - 4 = 2n + 7 and the variable used. (2 marks) Section B - Calculations and Applications (15 marks) 6. Solve: (i) x + 3 = 10 (ii) y - 7 = 12 (iii) 6z = 42 (iv) a/5 = 8 (v) 3n - 2 = 46 (vi) 20p/3 = 40. (3 marks) 7. Solve: (i) 4(m + 3) = 18 (ii) -2(x + 3) = 8 (iii) 3(n - 5) = 21. Check each answer. (3 marks) 8. Write equations for: (i) The sum of p and 4 is 15. (ii) Seven times m plus 7 gives 77. (iii) One-fourth of a number minus 4 gives 4. Solve each. (3 marks) 9. Write two different equations with solution x = 4 and two with y = -2. (3 marks) 10. Raju's father's age is 5 years more than three times Raju's age. His father is 44 years old. Form an equation and find Raju's age. (3 marks) Section C - Diagrams (10 marks) 11. Draw a weighing-scale (balance) diagram to show how 2x + 3 = 11 is solved step by step by removing equal weights from both pans. (4 marks) 12. Draw a flowchart showing the steps to solve 5t - 3 = 3t - 5 using transposition. (3 marks) 13. Draw a triangle whose angles are x, 2x and 3x. Form an equation using the angle sum property and find each angle. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. The perimeter of a rectangle is 34 cm and its length is 3 cm more than its breadth. (i) Let breadth be b; write the length. (ii) Form the equation. (iii) Solve for b. (iv) Find the length and area. (5 marks) 15. Irfan says he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (i) Form an equation. (ii) Find Parmit's marbles. (iii) Check your answer. (iv) If Parmit gets 4 more, how many more does Irfan need to keep the same relation? (5 marks) 16. A school gives prize money of Rs 2100 as 30 prizes in all: first prizes of Rs 100 each and second prizes of Rs 50 each. (i) Let first prizes be x; write the number of second prizes. (ii) Form an equation. (iii) Solve it. (iv) Find the number of each prize. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Verify every solution by substituting it back into the original equation.