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Chapter 9 | Linear Equations In One Variable | Class-8 DAV Secondary Mathematics
Worksheet 1: Questions and Solutions
Q1. Solve the following equations and check your answer.
(i) (p + 7)/(p − 6) = 1/3
Cross-multiplying: 3(p + 7) = p − 6 ⇒ 3p + 21 = p − 6 ⇒ 2p = −27
∴ p = −27/2
Check: LHS = (−13/2)/(−39/2) = 1/3 = RHS
(ii) (x − 2)/(6x + 1) = 1
Cross-multiplying: x − 2 = 6x + 1 ⇒ −5x = 3
∴ x = −3/5
Check: LHS = (−13/5)/(−13/5) = 1 = RHS
(iii) 3x/(5x − 5) = −1
Cross-multiplying: 3x = −(5x − 5) ⇒ 3x = −5x + 5 ⇒ 8x = 5
∴ x = 5/8
Check: LHS = (15/8)/(−15/8) = −1 = RHS
(iv) (2x − 1)/(5x) = −1/6
Cross-multiplying: 6(2x − 1) = −5x ⇒ 12x − 6 = −5x ⇒ 17x = 6
∴ x = 6/17
Check: LHS = (−5/17)/(30/17) = −1/6 = RHS
(v) (4x + 1)/(3x − 1) = −2
Cross-multiplying: 4x + 1 = −2(3x − 1) ⇒ 4x + 1 = −6x + 2 ⇒ 10x = 1
∴ x = 1/10
Check: LHS = 1.4/(−0.7) = −2 = RHS
(vi) (4z − 3)/(2z + 1) = 5/7
Cross-multiplying: 7(4z − 3) = 5(2z + 1) ⇒ 28z − 21 = 10z + 5 ⇒ 18z = 26
∴ z = 13/9
Check: LHS = (25/9)/(35/9) = 5/7 = RHS
(vii) ((2/5)x + 3)/((1/3)x − 1) = 3/5
Cross-multiplying: 5((2/5)x + 3) = 3((1/3)x − 1) ⇒ 2x + 15 = x − 3
∴ x = −18
Check: LHS = (−21/5)/(−7) = 3/5 = RHS
(viii) (2x − 3/4)/(3x + 4/5) = 1/5
Cross-multiplying: 5(2x − 3/4) = 3x + 4/5 ⇒ 10x − 15/4 = 3x + 4/5 ⇒ 7x = 4/5 + 15/4 = 91/20
∴ x = 13/20
Check: LHS = (11/20)/(55/20) = 1/5 = RHS
(ix) ((3/4)x + 1)/(x + 1/5) = 7/4
Cross-multiplying: 4((3/4)x + 1) = 7(x + 1/5) ⇒ 3x + 4 = 7x + 7/5 ⇒ 4x = 13/5
∴ x = 13/20
Check: LHS = (119/80)/(68/80) = 7/4 = RHS
(x) (3k + 5)/(4k − 3) = 4/9
Cross-multiplying: 9(3k + 5) = 4(4k − 3) ⇒ 27k + 45 = 16k − 12 ⇒ 11k = −57
∴ k = −57/11
Check: LHS = (−116/11)/(−261/11) = 4/9 = RHS
(xi) (0.5x − 4)/(2.4x + 6) = −5/3
Cross-multiplying: 3(0.5x − 4) = −5(2.4x + 6) ⇒ 1.5x − 12 = −12x − 30 ⇒ 13.5x = −18
∴ x = −4/3
Check: LHS = (−14/3)/(14/5) = −5/3 = RHS
(xii) (x/3 − 2/5)/(3/4 − 2x) = 16/15
Cross-multiplying: 15(x/3 − 2/5) = 16(3/4 − 2x) ⇒ 5x − 6 = 12 − 32x ⇒ 37x = 18
∴ x = 18/37
Check: LHS = (−44/185) ÷ (−33/148) = 16/15 = RHS
(xiii) [(1 − 2x) + (1 + 2x)]/[(4x + 1) + (x − 3)] = 1/2
Cross-multiplying: Numerator = 2, denominator = 5x − 2, so 2/(5x − 2) = 1/2 ⇒ 5x − 2 = 4 ⇒ 5x = 6
∴ x = 6/5
Check: LHS = 2/4 = 1/2 = RHS
(xiv) [x² − (x + 2)(x + 3)]/(7x + 1) = 2/3
Cross-multiplying: x² − (x² + 5x + 6) = −5x − 6, so 3(−5x − 6) = 2(7x + 1) ⇒ −15x − 18 = 14x + 2 ⇒ −29x = 20
∴ x = −20/29
Check: LHS = (−74/29)/(−111/29) = 2/3 = RHS
Q2. Find the positive value of the variable for which the given equation is satisfied.
(i) (3 − x²)/(8 + x²) = −3/4
Cross-multiplying: 4(3 − x²) = −3(8 + x²) ⇒ 12 − 4x² = −24 − 3x² ⇒ x² = 36
Taking the positive value, x = 6
(ii) (y² + 6)/(8y² + 3) = 1/5
Cross-multiplying: 5(y² + 6) = 8y² + 3 ⇒ 5y² + 30 = 8y² + 3 ⇒ 3y² = 27 ⇒ y² = 9
Taking the positive value, y = 3
(iii) (x² − 9)/(5 + x²) = 5/9
Cross-multiplying: 9(x² − 9) = 5(5 + x²) ⇒ 9x² − 81 = 25 + 5x² ⇒ 4x² = 106 ⇒ x² = 53/2
Taking the positive value, x = √(53/2) ≈ 5.15
(iv) (y² + 4)/(3y² + 7) = 1/2
Cross-multiplying: 2(y² + 4) = 3y² + 7 ⇒ 2y² + 8 = 3y² + 7 ⇒ y² = 1
Taking the positive value, y = 1
Handwritten working
The scanned pages below show the same Q1 and Q2 solved by hand.
- DAV class 8 Maths Book Solutions
- Chapter 1 | Square and Square Roots | Class-8 DAV Secondary Mathematics
- Chapter 2 | Cube and Cube Roots | Class-8 DAV Secondary Mathematics
- Chapter 3 | Exponents And Radicals | Class-8 DAV Secondary Mathematics
- Chapter 4 | Direct And Inverse Variation | Class-8 DAV Secondary Mathematics
- Chapter 5 | Profit, Loss And Discount | Class-8 DAV Secondary Mathematics
- Chapter 6 | Compound Interest | Class-8 DAV Secondary Mathematics
- Chapter 7 | Algebraic Identities | Class-8 DAV Secondary Mathematics
- Chapter 8 | Polynomials | Class-8 DAV Secondary Mathematics
- Chapter 9 | Linear Equations In One Variable | Class-8 DAV Secondary Mathematics
- Chapter 10 | Parallel Lines | Class-8 DAV Secondary Mathematics
- Chapter 11 | Understanding Quadrilaterals | Class-8 DAV Secondary Mathematics
- Chapter 12 | Construction Of Quadrilaterals | Class-8 DAV Secondary Mathematics
- Chapter 13 | Introduction To Graphs | Class-8 DAV Secondary Mathematics
- Chapter 14 | Mensuration | Class-8 DAV Secondary Mathematics
- Chapter 15 | Statistics and Probability | Class-8 DAV Secondary Mathematics
- Chapter 16 | Rotational Symmetry | Class-8 DAV Secondary Mathematics