Linear Equations in One Variable quiz

Which of the following is a linear equation in one variable?

The solution of 3x - 4 = 11 is:

If 2x + 5 = x + 9, then x is:

The solution of x/4 = 3 is:

If 5(x - 2) = 15, then x is:

When the term +7 is transposed from the left side to the right side of an equation, it becomes:

Two numbers differ by 5 and their sum is 25. The larger number is:

The solution of (x + 1)/2 = 3 is:

If 0.3y = 1.2, then y is:

The sum of three consecutive integers is 51. The smallest of them is:

Solve 7x - 9 = 19 and verify the solution. (2 marks)

Solve 8x + 4 = 3(x - 1) + 7. (2 marks)

Solve x = (4/5)(x + 10). (2 marks)

Solve (2x - 3)/(3x + 2) = -2/3. (2 marks)

When half of a number is added to 7, the result is 15. Find the number. (2 marks)

The length of a rectangle is 5 cm more than its breadth and its perimeter is 50 cm. Find its length and breadth. (2 marks)

The sum of two numbers is 95. If one exceeds the other by 15, find the numbers. (2 marks)

The base of an isosceles triangle is 4/3 cm and its perimeter is 62/15 cm. Find the length of each of the equal sides. (2 marks)

A father is three times as old as his son. The sum of their ages is 48 years. Find their ages. (2 marks)

Why can we multiply both sides of an equation by the same non-zero number? What goes wrong if we multiply both sides by zero? (2 marks)

Solve: (i) (x - 5)/3 = (x - 3)/5 (ii) (3t - 2)/4 - (2t + 3)/3 = 2/3 - t (iii) m - (m - 1)/2 = 1 - (m - 2)/3. (3 marks)

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number. (3 marks)

Lakshmi is a cashier in a bank. She has currency notes of Rs 100, Rs 50 and Rs 10 in the ratio 2 : 3 : 5, and the total cash is Rs 4,00,000. How many notes of each denomination does she have? (3 marks)

In a triangle, one angle is 20 degrees more than the smallest angle and the third angle is twice the smallest angle. Find all three angles. (3 marks)

The sum of three consecutive odd numbers is 147. Find the numbers and verify. (3 marks)

Read the passage and answer the questions. At a school fair, a ticket costs Rs 20 for a child and Rs 50 for an adult. The number of adults who came was 40 less than the number of children, and the total money collected from tickets was Rs 7,800. (i) Taking the number of children as c, form an equation. (ii) Solve the equation to find the number of children and the number of adults. (iii) Verify that the total collection is Rs 7,800. (5 marks)

Read the passage and answer the questions. Sonu's grandfather is 10 times as old as Sonu. He is also 54 years older than Sonu. (i) Form a linear equation, taking Sonu's age as x years. (ii) Find the present ages of Sonu and her grandfather. (iii) After how many years will the grandfather be 4 times as old as Sonu? (5 marks)

Read the passage and answer the questions. The length of a rectangular school garden is 2 m more than twice its breadth. The perimeter of the garden is 76 m, and it is to be fenced at Rs 50 per metre. (i) Form an equation taking the breadth as b metres. (ii) Find the length and breadth of the garden. (iii) Find the cost of fencing the garden. (5 marks)

Read the passage and answer the questions. Ravi spent one-fourth of his pocket money on books and one-third on clothes. He was left with Rs 250. (i) Form an equation taking his total pocket money as Rs x. (ii) Solve it to find his total pocket money. (iii) How much did he spend on books and on clothes? (5 marks)

Read the passage and answer the questions. Two cars start at the same time from two towns 300 km apart and travel towards each other. One car is 10 km/h faster than the other, and they meet after 3 hours. (i) Taking the speed of the slower car as x km/h, form an equation. (ii) Find the speed of each car. (iii) How far from each town do they meet? (5 marks)

Draw balance diagrams to show the solution of 4x + 3 = 2x + 11 step by step, writing the equation at each stage. Find x and verify the solution. State the rules used at each step. (6 marks)

Write the steps for solving a word problem using a linear equation. Use them to solve: (i) The sum of three consecutive multiples of 11 is 363; find the multiples. (ii) Two numbers are in the ratio 5 : 3 and they differ by 18; find the numbers. (6 marks)

Solve the following equations, showing how each is reduced to linear form: (i) (6x + 1)/3 + 1 = (x - 3)/6 (ii) (7y + 4)/(y + 2) = -4/3. Mark both solutions on a number line and verify each by substitution. (6 marks)

The length of a rectangle exceeds its breadth by 3 cm. If the length and the breadth are each increased by 2 cm, the area increases by 70 cm^2. Draw the original and the new rectangle, form an equation, show that it reduces to a linear equation, and find the original length and breadth. (6 marks)

(i) Box P weighs 2.5 kg more than box Q, and box R weighs 10.25 kg more than box Q. The total weight of the three boxes is 48.75 kg. Draw a bar model, form an equation and find the weight of each box. (ii) Amina thinks of a number, subtracts 5/2 from it and multiplies the result by 8. The result is 3 times the number she thought of. Find the number. (6 marks)