Students can Download Class 8 Maths Chapter 8 Linear Equations in One Variable Ex 8.1 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 8 Maths Chapter 8 Linear Equations in One Variable Ex 8.1

1. Solve the following :

Question i.

x + 3 = 11

Answer:

x + 3 = 11

x = 11 – 3

x = 8

Question ii.

y – 9 = 21

Answer:

y – 9 = 21

y = 21 + 9

y = 30

Question iii.

10 = z + 3

Answer:

10 = z + 3 10 – 3 = z

7 = z or z = 7

Question iv.

\(\frac{3}{11}+x=\frac{9}{11}\)

Answer:

Question v.

10x = 30

Answer:

10x = 30

x = \(\frac{30}{10}\)

x = 3

Question vi.

\(\frac{s}{7}=4\)

Answer:

\(\frac{s}{7}=4\)

S = 4 × 7

S = 28

Question vii.

\(\frac{3 x}{6}=10\)

Answer:

\(\frac{3 x}{6}=10\)

3x = 10 × 6

3x = 60

x = \(\frac{60}{3}\)

x = 20

Question viii.

\(1.6=\frac{x}{1.5}\)

Answer:

\(1.6=\frac{x}{1.5}\)

1.6 × 1.5 = x

2.40 = x

x = 2.4

Question ix.

8x – 8 = 48

Answer:

8x – 8 = 48

8x = 48 + 8

8x = 56

x = \(\frac{56}{8}\)

x = 7

Question x.

\(\frac{x}{3}+1=\frac{7}{15}\)

Answer:

8x = 48 + 8

8x = 56

\(x=\frac{56}{8}\)

x = 7

Question xi.

\(\frac{x}{5}=12\)

Answer:

\(\frac{x}{5}=12\)

x = 12 × 5

x = 60

Question xii.

\(\frac{3 x}{5}=15\)

Answer:

Question xiii.

3(x + 6) = 24

Answer:

3(x + 6) = 24

3x + 18 = 24

3x = 24 – 18

3x = 6

x = \(\frac{6}{3}\) = 2

Question xiv.

\(\frac{x}{4}-8=1\)

Answer:

Question xv.

3(x + 2) – 2(x – 1) = 7

Answer:

3(x + 2) – 2(x – 1) = 7

3x + 6 – 2x + 2 = 7

x + 8 = 7 .

x = 7 – 8

x = – 1

2. Solve the equations :

Question i.

5x = 3x + 24

Answer:

5x = 3x + 24

2x = 24

x = \(\frac{24}{2}\)

x = 12

Question ii.

8t + 5 = 2t – 31

Answer:

8t + 5 = 2t – 31

6t = – 36

t = \(\frac{-36}{6}\)

t = – 6

Question iii.

7x – 10 = 4x + 11

Answer:

7x – 10 = 4x + 11

7x – 4x = 11 + 10

3x = 21

x = \(\frac{21}{3}\)

x = 7

Question iv.

4z + 3 = 6 + 2z

Answer:

4z + 3 = 6 + 2z

4z – 2z = 6 – 3

2z = 3

Question v.

2x – 1 = 14 – x

Answer:

2x – 1 = 14 – x

2x + x = 14 + 1

3x = 15

x = \(\frac{15}{3}\)

x = 5

Question vi.

6x + 1 = 3(x -1) + 7

Answer:

6x + 1 = 3(x – 1) + 7

6x + 1 = 3x – 3 + 7

6x + 1 = 3x + 4

6x – 3x = 4 – 1

3x = 3

x = \(\frac{3}{3}\)

x = 1

Question vii.

\(\frac{2 x}{5}-\frac{3}{2}=\frac{x}{2}+1\)

Answer:

Question viii.

\(\frac{x-3}{5}-2=\frac{2 x}{5}\)

Answer:

Question ix.

3(x + 1) = 12 + 4(x – 1)

Answer:

3(x + 1) = 12 + 4(x – 1)

3x + 3 = 12 + 4x – 4

3x + 3 = 4x + 8

3x – 4x = 8 – 3

-x = 5

x = -5

Question x.

2x – 5 = 3(x – 5)

Answer:

2x – 5 = 3(x – 5)

2x – 5 = 3x – 15

2x – 3x = -15 + 5

-x = -10

x= 10

Question xi.

6(1 – 4x) + 7(2 + 5x) = 53

Answer:

6( 1 – 4x) + 7(2 + 5x) = 53

6 – 24x + 14 + 35x = 53

35x – 24x + 6 + 14 = 53

11x + 20 = 53

11x = 53 – 20

x = \(\frac{33}{11}\)

x = 3

Question xii.

3(x + 6) + 2(x + 3) = 64

Answer:

3(x + 6) + 2(x + 3) = 64

3x + 18 + 2x + 6 = 64

3x + 2x + 18 + 6 = 64

5x + 24 = 64

5x = 64 – 24

5x = 40

x = \(\frac{40}{5}\)

∴ x = 8.

Question xiii.

\(\frac{2 m}{3}+8=\frac{m}{2}-1\)

Answer:

Question xiv.

\(\frac{3}{4}(x-1)=(x-3)\)

Answer:

\(\frac{3}{4}(x-1)=(x-3)\)

3(x – 1) = 4(x – 3)

3x – 3 = 4x – 12

3x – 4x = -12 + 3

– x = – 9

x = 9