5 Mark Question

Question 15 Marks

6(1 - 4x) + 7(2 + 5x) = 53

Answer

6(1 - 4x) + 7(2 + 5x) = 53
On expanding the brackets, we get (6 × 1) - (6 × 4x) + (7 × 2) + (7 × 5x) = 53
6 - 24x + 14 + 35x = 53
6 + 14 + 35x - 24x = 53
20 + 11x = 53
Subtracting 20 from both sides, we get 20 + 11x - 20 = 53 - 20
11x = 33
Dividing both sides by 11, we get
$\frac{\text{11x}}{11}=\frac{33}{11}$
$\text{x}=3$
Verification:
Substituting x = 3 in L.H.S., we get
= 6(1 - 4 × 3) + 7(2 + 5 × 3)
= 6(1 - 12) + 7(2 + 15)
= 6(-11) + 7(17)
= -66 + 119
= 53 = R.H.S.
L.H.S. = R.H.S.
Hence, verified.

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Question 25 Marks

5(2 - 3x) - 17(2x - 5) = 16

Answer

5(2 - 3x) - 17(2x - 5) = 16
On expanding the brackets, we get (5 × 2) - (5 × 3x) - (17 × 2x) + (17 × 5) = 16
10 - 15x - 34x + 85 = 16
10 + 85 - 34x - 15x = 16
95 - 49x = 16
Subtracting 95 from both sides, we get -49x + 95 - 95 = 16 - 95
-49x = -79
Dividing both sides by -49, we get
$\frac{-49\text{x}}{49}=\frac{-79}{-49}$
$\text{x}=\frac{79}{49}$
Verification:
Substituting $\text{x}=\frac{79}{49}$ in L.H.S., we get
$=5\Big(2-3\times\frac{79}{49}\Big)-17\Big(2\times\frac{79}{49}-5\Big)$
$=(5\times2)-\Big(5\times3\times\frac{79}{49}\Big)-\Big(17\times2\times\frac{79}{49}\Big)+(17\times5)$
$=10-\frac{1185}{49}-\frac{2686}{49}+85$
$=\frac{490-1185-2686+4165}{49}=\frac{784}{49}=16=\text{R.H.S.}$
$\text{L.H.S.}=\text{R.H.S.}$
Hence, verified.

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Question 35 Marks

$14=\frac{7\text{x}}{10}-8$

Answer

$14=\frac{7\text{x}}{10}-8$
Adding 8 to both sides, we get
$14+8=\frac{7\text{x}}{10}-8+8$
$22=\frac{7\text{x}}{10}$
Multiplying both sides by 10, we get
$22\times10=\frac{7\text{x}}{10}\times10$
$220=7\text{x}$
Dividing both sides by 7, we get
$\frac{220}{7}=\frac{7\text{x}}{7}$
$\text{x}=\frac{220}{7}$
Verfication:
Substituting $\text{x}=\frac{220}{7}$ R.H.S., we get
L.H.S. = 14 and $\text{R.H.S.}=\frac{\frac{220}{7}}{\frac{7}{10}}10-8$
$=\frac{220}{10}-8$
$=22-8=14$
L.H.S. = R.H.S.
Hence, verified.

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Question 45 Marks

8(2x - 5) - 6(3x - 7) = 1

Answer

8(2x - 5) - 6(3x - 7) = 1On expanding the brackets, we get (8 × 2x) - (8 × 5) - (6 × 3x) + (-6) × (-7) = 1
16x - 40 - 18x + 42 = 1
16x - 18x + 42 - 40 = 1
-2x + 2 = 1
Subtracting 2 from both sides, we get
-2x+ 2 - 2 = 1 - 2
-2x = -1
Multiplying both sides by -1, we get
-2x × (-1) = -1 × (-1)
2x = 1
Dividing both sides by 2, we get
$\frac{2\text{x}}{2}=\frac12$
$\text{x}=\frac12$
Verification:
Substituting $\text{x}=\frac12$ in L.H.S., we get
$=8\Big(2\times\frac{1}{2}-5\Big)-6\Big(3\times\frac{1}{2}-7\Big)$
$= 8(1 - 5) - 6(32 - 7)$
$= 8× (-4) - (6 \times 32) + (6 \times 7) $
$= -32 - 9 + 42 $
$= - 41 + 42 = 1 = \text{R.H.S.}$
$\text{L.H.S.} = \text{R.H.S.}$
Hence, verified.

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Question 55 Marks

$\frac{\text{x}-3}{5}-2=-1$

Answer

$\frac{\text{x}-3}{5}-2=-1$
Adding 2 to both sides, we get
$\frac{\text{x}-3}{5}-2+2=-1+2$
$\frac{\text{x}-3}{5}=1$
Multiplying both sides by 5, we get
$\frac{\text{x}-3}{5}\times5=1\times5$
$\text{x}-3=5$
Adding 3 to both sides, we get
x - 3 + 3 = 5 + 3
x = 8
Verification:
Substituting x = 8 in L.H.S., we get
$=\frac{8-3}{5}-2=\frac{5}{5}-2=1-2=-1=\text{R.H.S.}$
Hence, verified.

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Question 65 Marks

$\frac{1}{3}-\text{2x}=0$

Answer

$\frac{1}{3}-\text{2x}=0$
Subtracting 13 from both sides, we get
$\frac{1}{3}-2\text{x}-\frac13=0-\frac13$
$-2\text{2x}=-\frac13$
Multiplying both sides by -1, we get
$-2\text{x}\times(-1)=-\frac{1}{3}\times(-1)$
$2\text{x}=\frac13$
Dividing both sides by 2, we get
$\frac{2\text{x}}{2}=\frac{\frac13}{2}$
$\text{x}=\frac16$
Verification:
Substituting $\text{x}=\frac16$ in L.H.S., we get
$\text{L.H.S.}=\frac13-2\times\frac16=\frac13-\frac13=0,$ and $\text{R.H.S.}=0$
$\text{L.H.S.}=\text{R.H.S.}$
Hence Verified.

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Maths 5 Mark Question

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