Selina solutions

Selina solutions

Grade 6

Simple (Linear) Equations (Including Word Problems) | Revision Exercise

Question 1

Q1) Solve each of the following equations:

(i) 2x + 3 = 7

(ii) 2x - 3 = 7

(iii) 2x ÷ 3 = 7

(iv) 3x - 8 - 13

(v) 3y + 8 = 13

(vi) 3y ÷ 8 = 13

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

(viii) \frac{3}{5}x+4=13

(ix) u+3\frac{1}{4}=4\frac{1}{3}

(x) 5x – 2.4 = 4.9

(xi) 5y + 4.9 = 2.4

(xii) 48 z + 3.6 = 1.2

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

(xiv) \frac{y}{3}+7=2

(xv) \frac{2m}{3}=8\frac{2}{3}

(xvi) -3x + 4 = 10

(xvii) 5 = x - 3

(xviii) 8y = 3 - 3y

(xix) 4x + 4.9 = 6.5

(xx) 3z + 2 = -4

(xxi) 7y - 18 = 17

(xxii) \frac{x}{1.2}-6=1

(xxiii) \frac{z}{2.4}+3.6=5.1

(xxiv) \frac{y}{1.8}-2.1=-2.8

(xxv) 7x – 2 = 4x + 7

(xvi) 3y -(y + 2) = 4

(xxvii) 3z – 18 = z – (12 – 4z)

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

(xxix) 3\frac{2}{3}-y=2\frac{1}{2}

(xxx) 2z-2\frac{1}{2}=3\frac{1}{2}

(xxxi) 5x – 2x + 15 = 27

(xxxii) 5y – 15 = 27 -2y

(xxxiii) 7z + 15 = 3z – 13

(xxxiv) 2 (x -3) – 3 (x-4) =12

(xxxv) (7y + 8) + 7 = 8

(xxxvi) 2(z – 5) +3 (z + 2) -(3 – 5z) = 10

Solution 1:

(i) 2x + 3 = 7

2x = 7 - 3

2x = 4

x = 2

(ii) 2x - 3 = 7

2x = 7 + 3

2x = 10

x = 5

(iii) 2x ÷ 3 = 7

\frac{2x}{3}=7

2x=7\times3

2x=21

x=\frac{21}{2}=10\frac{1}{2}

(iv) 3y - 8 = 13

3y - 8 + 8 = 13 + 8

(Adding 8 to both sides)

3y = 21

y = 7

(v) 3y + 8 = 13

3y + 8 - 8 = 13 - 8

(Subtracting 8 from both sides)

3y = 5

y=\frac{5}{3}=1\frac{2}{3}

(vi) 3y ÷ 8 = 13

\frac{3y}{8}=13

Multiplying by 8

3y=13\times8

3y = 104

y=\frac{104}{3}=34\frac{2}{3}

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

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

x=8\frac{1}{2}

(viii) \frac{3}{5}x+4=13

\frac{3}{5}x+4-4=13-4

\frac{3}{5}x=9

x=9\times\frac{5}{3}=15

(ix) u+3\frac{1}{4}=4\frac{1}{3}

u+\frac{13}{4}=\frac{13}{3}

u=\frac{13}{3}-\frac{13}{4}

u=\frac{13\times4-13\times3}{12}=\frac{52-39}{12}

u=\frac{13}{12}=1\frac{1}{12}

(x) 5x - 2.4 = 4.9

5x - 2.4 + 2.4 = 4.9 + 2.4

(Adding 2.4 to both sides)

5x = 7.3

x=\frac{7.3}{5}=1.46

(xi) 5y + 4.9 = 2.4

5y + 4.9 - 4.9 = 2.4 - 4.9

(Subtracting 4.9 from both sides)

5y = -2.5

y = -0.5

(xii) 4.8z + 3.6 = 1.2

4.8z + 3.6 - 3.6 = 1.2 - 3.6

(Subtracting 3.6 from both sides)

4.8z = -2.4

z = -0.5

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

\frac{x}{2}=5+3

\frac{x}{2}=8

x=2\times8=16

(xiv) \frac{y}{3}+7=2

\frac{y}{3}=2-7

\frac{y}{3}=-5

y=3\times\left(-5\right)\ =\ -15

(xv) \frac{2m}{3}=8\frac{2}{3}

\frac{2m}{3}=\frac{26}{3}

2m = 26

m = 13

(xvi) -3x + 4 = 10

3x + 4 - 4 = 10 - 4’

(Subtracting 4 from both sides)

-3x = 6

x = -2

(xvii) 5 = x - 3

5 + 3 = x -3 + 3

(Adding 3 to both sides)

8 = x

(xviii) 8y = 3 - 3y

18 - 3 = 3 - 3y - 3

(Subtracting 3 from both sides)

15 = - 3y

y = -5

(xix) 4x + 4.9 = 6.5

4x + 4.9 - 4.9 = 6.5 - 4.9

(Subtracting 4.9 from both sides)

4x = 1.6

x = 0.4

(xx) 3z + 2 = -4

3z + 2 - 2 = -4 - 2

(Subtracting -2 from both sides)

3z = -6

z = -2

(xxi) 7y - 18 = 17

7y - 18 + 18 = 17 + 18

(Adding 18 to both sides)

7y = 35

y = 5

(xxii) \frac{x}{1.2}-6=1

\frac{x}{1.2}=1+6

x=7\times1.2=8.4

(xxiii) \frac{z}{2.4}+3.6=5.1

\frac{z}{2.4}=5.1-3.6

z=1.5\times2.4

z = 3.60

(xxiv) \frac{y}{1.8}-2.1=-2.8

\frac{y}{1.8}=-2.8+2.1

y=-0.7\times1.8

y = -1.26

(xxv) 7x - 2 = 4x + 7

7x - 2 + 2 = 4x + 7 + 2

(Adding 2 to both sides)

7x = 4x + 9

7x - 4x = 4x + 9 - 4x

(Subtracting 4x from both sides)

3x = 9

x = 3

(xxvi) 3y -(y + 2) = 4

3y - (y + 2) = 4

3y - y - 2 = 4

2y - 2 = 4

2y - 2 + 2 = 4 + 2

(Adding 2 to both sides)

2y = 6

(Dividing by 2)

y = 3

(xxvii) 3z – 18 = z – (12 – 4z)

3z – 18 = z – (12 – 4z)

3z – 18 = z – 12 + 4z

3z - 18 = 5z - 12

3z - 18 + 18 = 5z - 12 + 18

(Adding 18 to both sides)

3z = 5z + 6

3z - 5z = 5z + 6 - 5z

(subtracting 5z from both sides)

-2z = 6

(Dividing by -2)

z = -3

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

x=\frac{11}{2}+\frac{5}{2}=\frac{16}{2}=8

(xxix) 3\frac{2}{3}-y=2\frac{1}{2}

\frac{17}{5}-\frac{5}{2}=y

y=\frac{17\times2-5\times5}{10}

y=\frac{34-25}{10}=\frac{9}{10}

(xxx) 2z-2\frac{1}{2}=3\frac{1}{2}

2z=\frac{7}{2}+\frac{5}{2}=\frac{12}{2}=6

2z = 6

z = 3

(xxxi) 5x - 2x + 15 = 27

3x = 27 - 15

3x = 12

x = 4

(xxxii) 5y – 15 = 27 -2y

5y + 2y = 27 + 15

7y = 42

y = 6

(xxxiii) 7z + 15 = 3z – 13

7z - 3z = - 13 - 15

4z = - 28

z = - 7

(xxxiv) 2 (x -3) – 3 (x-4) =12

2x - 6 - 3x + 12 = 12

2x - 3x = 12 - 12 + 6

x = 6

x = - 6

(xxxv) (7y + 8) ÷ 7 = 8

\frac{7y+8}{7}=8

7y\ +\ 8=\ 56

7y = 56 - 8

7y = 48

y\ =\ \frac{48}{7}=6\frac{6}{7}

(xxxvi) 2(z – 5) +3 (z + 2) -(3 – 5z) = 10

2z - 10 + 3z + 6 - 3 + 5z = 10

2z + 3z + 5z = 10 + 10 - 6 + 3

10z = 17

z=\frac{17}{10}=1\frac{7}{10}

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Question 1

Q1) Solve each of the following equations:

(i) 2x + 3 = 7

(ii) 2x - 3 = 7

(iii) 2x ÷ 3 = 7

(iv) 3x - 8 - 13

(v) 3y + 8 = 13

(vi) 3y ÷ 8 = 13

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

(viii) \frac{3}{5}x+4=13

(ix) u+3\frac{1}{4}=4\frac{1}{3}

(x) 5x – 2.4 = 4.9

(xi) 5y + 4.9 = 2.4

(xii) 48 z + 3.6 = 1.2

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

(xiv) \frac{y}{3}+7=2

(xv) \frac{2m}{3}=8\frac{2}{3}

(xvi) -3x + 4 = 10

(xvii) 5 = x - 3

(xviii) 8y = 3 - 3y

(xix) 4x + 4.9 = 6.5

(xx) 3z + 2 = -4

(xxi) 7y - 18 = 17

(xxii) \frac{x}{1.2}-6=1

(xxiii) \frac{z}{2.4}+3.6=5.1

(xxiv) \frac{y}{1.8}-2.1=-2.8

(xxv) 7x – 2 = 4x + 7

(xvi) 3y -(y + 2) = 4

(xxvii) 3z – 18 = z – (12 – 4z)

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

(xxix) 3\frac{2}{3}-y=2\frac{1}{2}

(xxx) 2z-2\frac{1}{2}=3\frac{1}{2}

(xxxi) 5x – 2x + 15 = 27

(xxxii) 5y – 15 = 27 -2y

(xxxiii) 7z + 15 = 3z – 13

(xxxiv) 2 (x -3) – 3 (x-4) =12

(xxxv) (7y + 8) + 7 = 8

(xxxvi) 2(z – 5) +3 (z + 2) -(3 – 5z) = 10

Solution 1:

(i) 2x + 3 = 7

2x = 7 - 3

2x = 4

x = 2

(ii) 2x - 3 = 7

2x = 7 + 3

2x = 10

x = 5

(iii) 2x ÷ 3 = 7

\frac{2x}{3}=7

2x=7\times3

2x=21

x=\frac{21}{2}=10\frac{1}{2}

(iv) 3y - 8 = 13

3y - 8 + 8 = 13 + 8

(Adding 8 to both sides)

3y = 21

y = 7

(v) 3y + 8 = 13

3y + 8 - 8 = 13 - 8

(Subtracting 8 from both sides)

3y = 5

y=\frac{5}{3}=1\frac{2}{3}

(vi) 3y ÷ 8 = 13

\frac{3y}{8}=13

Multiplying by 8

3y=13\times8

3y = 104

y=\frac{104}{3}=34\frac{2}{3}

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

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

x=8\frac{1}{2}

(viii) \frac{3}{5}x+4=13

\frac{3}{5}x+4-4=13-4

\frac{3}{5}x=9

x=9\times\frac{5}{3}=15

(ix) u+3\frac{1}{4}=4\frac{1}{3}

u+\frac{13}{4}=\frac{13}{3}

u=\frac{13}{3}-\frac{13}{4}

u=\frac{13\times4-13\times3}{12}=\frac{52-39}{12}

u=\frac{13}{12}=1\frac{1}{12}

(x) 5x - 2.4 = 4.9

5x - 2.4 + 2.4 = 4.9 + 2.4

(Adding 2.4 to both sides)

5x = 7.3

x=\frac{7.3}{5}=1.46

(xi) 5y + 4.9 = 2.4

5y + 4.9 - 4.9 = 2.4 - 4.9

(Subtracting 4.9 from both sides)

5y = -2.5

y = -0.5

(xii) 4.8z + 3.6 = 1.2

4.8z + 3.6 - 3.6 = 1.2 - 3.6

(Subtracting 3.6 from both sides)

4.8z = -2.4

z = -0.5

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

\frac{x}{2}=5+3

\frac{x}{2}=8

x=2\times8=16

(xiv) \frac{y}{3}+7=2

\frac{y}{3}=2-7

\frac{y}{3}=-5

y=3\times\left(-5\right)\ =\ -15

(xv) \frac{2m}{3}=8\frac{2}{3}

\frac{2m}{3}=\frac{26}{3}

2m = 26

m = 13

(xvi) -3x + 4 = 10

3x + 4 - 4 = 10 - 4’

(Subtracting 4 from both sides)

-3x = 6

x = -2

(xvii) 5 = x - 3

5 + 3 = x -3 + 3

(Adding 3 to both sides)

8 = x

(xviii) 8y = 3 - 3y

18 - 3 = 3 - 3y - 3

(Subtracting 3 from both sides)

15 = - 3y

y = -5

(xix) 4x + 4.9 = 6.5

4x + 4.9 - 4.9 = 6.5 - 4.9

(Subtracting 4.9 from both sides)

4x = 1.6

x = 0.4

(xx) 3z + 2 = -4

3z + 2 - 2 = -4 - 2

(Subtracting -2 from both sides)

3z = -6

z = -2

(xxi) 7y - 18 = 17

7y - 18 + 18 = 17 + 18

(Adding 18 to both sides)

7y = 35

y = 5

(xxii) \frac{x}{1.2}-6=1

\frac{x}{1.2}=1+6

x=7\times1.2=8.4

(xxiii) \frac{z}{2.4}+3.6=5.1

\frac{z}{2.4}=5.1-3.6

z=1.5\times2.4

z = 3.60

(xxiv) \frac{y}{1.8}-2.1=-2.8

\frac{y}{1.8}=-2.8+2.1

y=-0.7\times1.8

y = -1.26

(xxv) 7x - 2 = 4x + 7

7x - 2 + 2 = 4x + 7 + 2

(Adding 2 to both sides)

7x = 4x + 9

7x - 4x = 4x + 9 - 4x

(Subtracting 4x from both sides)

3x = 9

x = 3

(xxvi) 3y -(y + 2) = 4

3y - (y + 2) = 4

3y - y - 2 = 4

2y - 2 = 4

2y - 2 + 2 = 4 + 2

(Adding 2 to both sides)

2y = 6

(Dividing by 2)

y = 3

(xxvii) 3z – 18 = z – (12 – 4z)

3z – 18 = z – (12 – 4z)

3z – 18 = z – 12 + 4z

3z - 18 = 5z - 12

3z - 18 + 18 = 5z - 12 + 18

(Adding 18 to both sides)

3z = 5z + 6

3z - 5z = 5z + 6 - 5z

(subtracting 5z from both sides)

-2z = 6

(Dividing by -2)

z = -3

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

x=\frac{11}{2}+\frac{5}{2}=\frac{16}{2}=8

(xxix) 3\frac{2}{3}-y=2\frac{1}{2}

\frac{17}{5}-\frac{5}{2}=y

y=\frac{17\times2-5\times5}{10}

y=\frac{34-25}{10}=\frac{9}{10}

(xxx) 2z-2\frac{1}{2}=3\frac{1}{2}

2z=\frac{7}{2}+\frac{5}{2}=\frac{12}{2}=6

2z = 6

z = 3

(xxxi) 5x - 2x + 15 = 27

3x = 27 - 15

3x = 12

x = 4

(xxxii) 5y – 15 = 27 -2y

5y + 2y = 27 + 15

7y = 42

y = 6

(xxxiii) 7z + 15 = 3z – 13

7z - 3z = - 13 - 15

4z = - 28

z = - 7

(xxxiv) 2 (x -3) – 3 (x-4) =12

2x - 6 - 3x + 12 = 12

2x - 3x = 12 - 12 + 6

x = 6

x = - 6

(xxxv) (7y + 8) ÷ 7 = 8

\frac{7y+8}{7}=8

7y\ +\ 8=\ 56

7y = 56 - 8

7y = 48

y\ =\ \frac{48}{7}=6\frac{6}{7}

(xxxvi) 2(z – 5) +3 (z + 2) -(3 – 5z) = 10

2z - 10 + 3z + 6 - 3 + 5z = 10

2z + 3z + 5z = 10 + 10 - 6 + 3

10z = 17

z=\frac{17}{10}=1\frac{7}{10}

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