Question

Solve each of the following linear equations and also check the solution.
1. 5(3 - 3) - 4(x - 2) = 0
2. 8(x - 1) = 3(x - 1) + 17
3. 15(y - 4) – 2(y - 9) + 5(y + 6) = 0 [NCERT] 4. 0.25(4-3) = 0.05(10f - 9)
5. 4(3p + 2) –5(6p - 1) = 2(p - 8) - 6(7p -- 4)
INC
6. 3(5x - 7) + 2(9x -11) = 4(8x -7) -111
[NC
1
7. 0.16(5x - 2) = 0.4 x + 7 [NCERT Exemplar]
8. 2p -
=p-
2
2
1
х
9.
у
+
3 4
10.
-
3x5x
+
4 6
11. 1 +
+ 6(4x - 2) = 5
11
2 5
2
3​

Answer 1

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C0rRecT QueSti0n -

Solve each of the following linear equations and also check the solution.

$1 . \: 5(x - 3) - 4(x - 2) = 0 \\ \\ 2 . \: 8(x - 1) = 3(x - 1) + 17 \\ \\ 3 . \: 15(y - 4) - 2(y - 9) + 5(y + 6) = 0 \\ \\ 4 . \: 0.25(f-3) = 0.05(10f - 9) \\ \\ 5 . \: 4(3p + 2) - 5(6p - 1) = 2(p - 8) - 6(7p - 4) \\ \\ 6. \: 3(5x - 7) + 2(9x -11) = 4(8x -7) -11 \\ \\7 . \: 0.16(5x - 2) = 0.4 x + 7$

S0LUti0n -

$\\ \\ 1 => 5x - 6 - 4x +8 = 0 \\ \\ => x - 2 = 0 \\ \\ => x = 2 \\ \\ 2 => 8 x - 8 = 3x - 3 + 17 \\ \\ => 5x = 17 + 5 = 22 \\ \\ => x = \dfrac{22}{7} \\ \\ 3 => 15y - 60 - 2y + 18 + 5y + 30 = 0 \\ \\ => 18y = 12 \\ \\ => y = \dfrac { 12 }{ 18 } \\ \\ => y = \dfrac{ 4 \times \cancel{6} }{ 3 \times \cancel{6} } = \dfrac{4}{3} \\ \\ 4 => 25f - 75 = 50f - 45 \\ \\ => 25f = -30 \\ \\ => f = \dfrac{-30}{25} \\ \\ => f = \dfrac{ -6 \times \cancel{5} }{ 5 \times \cancel{5} } = \dfrac{ -6 }{ 5 } \\ \\ 5 => 12p + 8 - 30 p + 5 = 2p - 16 - 42p + 24 \\ \\ => 22p = -5 \\ \\ => p = \dfrac{ -5}{ 22 } \\ \\ 6 => 15x - 21 + 18x - 22 = 32x - 39 \\ \\ => x = 3 \\ \\ 7 => 0.8 x - 0.32 = 0.4 x + 7 \\ \\ => 0.4 x = 7</p><p>32 \\ \\ => x = \dfrac{7.32}{40} = 18.3$

Answer 2

Solve each of the following linear equations and also check the solution.

1. 5(3 - 3) - 4(x - 2) = 0

2. 8(x - 1) = 3(x - 1) + 17

3. 15(y - 4) – 2(y - 9) + 5(y + 6) = 0

4. 0.25(4-3) = 0.05(10f - 9)

5. 4(3p + 2) –5(6p - 1) = 2(p - 8) - 6(7p - 4)

6. 3(5x - 7) + 2(9x -11) = 4(8x -7) -111

1. 5(3 - 3) - 4(x - 2) = 0

⇒5(0) - 4x + 8 = 0

⇒8 - 4x = 9

⇒4x = 8

⇒x = 8/4

⇒x = 2

2. 8(x - 1) = 3(x - 1) + 17

⇒8x - 8 = 3x - 3 + 17

⇒8x - 3x = 17 + 8 - 3

⇒5x = 22

⇒x = 22/5

3. 15(y - 4) - 2(y - 9) + 5(y + 6) = 0

⇒15y - 60 - 2y + 18 + 5y + 30 = 0

⇒18y = 60 - 18 - 30

⇒18y = 12

⇒y = 12/18

⇒y = 2/3

4. 0.25(4-3) = 0.05(10f - 9)

⇒0.25*1 = 0.5f - 0.45

⇒0.25 + 0.45 = 0.5f

⇒0.7 = 0.5f

⇒f = 0.7/0.5

⇒f = 1.4

5. 4(3p + 2) - 5(6p - 1) = 2(p - 8) - 6(7p - 4)

⇒16.2p + 10.8 - 30p + 5 = 2p - 16 - 42p + 24

⇒16.2p - 30p - 2p - 42p = 24 - 16 - 5 - 10.8

⇒ -57.8p = -7.8

⇒p = -7.8/-57.8

⇒p = 7.8/57.8

6.3(5x - 7) + 2(9x -11) = 4(8x -7) -111

⇒31.5x - 44.1 + 18x - 22 = 32x - 28 - 111

⇒49.5x - 32x -44.1 - 22 + 28 + 111 = 0

⇒17.5x + 72.9 = 0

⇒17.5x = -72.9

⇒x = -72.9/17.5