Question

solve with explanation... ​

Answer 1

QUESTION:

Solve for x and check the answer.

a) 4x - ( 3x/2 ) = 15

b) 2x - 13 = - 3x/5

c) (x/5) - (x/6) = 4

d) (x/2) - 3 = (x/3) + 5

e) 2/7 ( x - 9) = 3 - (x/3)

f) x/3 + x/5 + x/15 = 3

g) 0.4 (3x - 1) = 0.5x + 1

h) (x + 1) / 4 = (x - 2) / 3

EXPLANATION:

a) 4x - ( 3x/2 ) = 15

$\frac{8x - 3x}{2} = 15 \\ \\ 5x = 30 \\ \\ x = 6$

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b) 2x - 13 = - 3x/5

10x - 65 = - 3x

13x = 65

x = 5

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$c)\:\:\frac{x}{5} - \frac{x}{6} = 4 \\ \\ \frac{6x - 5x}{30} = 4 \\ \\ x = 120$

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$d)\:\:\frac{x}{2} - 3 = \frac{x}{3} + 5 \\ \\ \frac{x}{2} - \frac{x}{3} = 5 + 3 \\ \\ \frac{3 x - 2x}{6} = 8 \\ \\ x = 48$

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$e)\:\:\frac{2}{7} (x - 9) = 3 - \frac{x}{3} \\ \\ x - 9 = \frac{7}{2} \bigg( \frac{9 - x}{3} \bigg) \\ \\x - 9 = \frac{63 - 7x}{6} \\ \\ x + \frac{7x}{6} = \frac{63}{6} + 9 \\ \\ \frac{6x + 7x}{6} = \frac{63 + 54}{6} \\ \\ 13x = 117 \\ \\ x = 9$

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$f)\:\:\frac{x}{3} + \frac{x}{5} + \frac{x}{15} = 3 \\ \\ \frac{5x + 3x + x}{15} = 3 \\ \\ 9x = 45 \\ \\ x = 5$

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g) 0.4 (3x - 1) = 0.5x + 1

1.2 x - 0.4 = 0.5x + 1

0.7x = 1.4

x = 2

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$h)\:\:\frac{x+ 1}{4} = \frac{x - 2}{3} \\ \\ 3(x + 1) = 4((x - 2) \\ \\ 3x + 3 = 4x - 8 \\ \\ - x = - 11 \\ \\ x = 11$

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VERIFICATION:

a) Substitute x = 6 in 4x - ( 3x/2 ) = 15

4(6) - 3(6)/2 = 15

24 - 18/2 = 15

24 - 9 = 15

15 = 15

Hence verified.

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b) Substitute x = 5 in 2x - 13 = - 3x/5

2(5) - 13 = - 3 (5)/5

10 - 13 = - 3 (1)

- 3 = - 3

Hence verified.

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c) Substitute x = 120 in (x/5) - (x/6) = 4

120/5 - 120/6 = 4

24 - 20 = 4

4 = 4

Hence verified.

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d) Substitute x = 48 in (x/2) - 3 = (x/3) + 5

(48/2) - 3 = (48/3) - 5

24 - 3 = 16 + 5

21 = 21

Hence verified.

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e) Substitute x = 9 in 2/7 ( x - 9) = 3 - (x/3)

2/7 ( 9 - 9) = 3 - (9/3)

2/7 ( 0) = 3 - 3

0 = 0

Hence verified.

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f) Substitute x = 5 in x/3 + x/5 + x/15 = 3

$\frac{5}{3} + \frac{5}{5} + \frac{5}{15} = 3 \\ \\ \frac{5}{3} + 1 + \frac{1}{3} = 3 \\ \\ \frac{5 + 3 + 1}{3} = 3 \\ \\ \frac{9}{3 } = 3 \\ \\ 3 = 3$

Hence verified.

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g) Substitute x = 2 in 0.4(3x - 1) = 0.5x + 1

0.4 (3(2) - 1) = 0.5(2)+ 1

0.4(6 - 1) = 1 + 1

(0.4)5 = 2

2 = 2

Hence verified.

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h) Substitute x = 11 in (x + 1) / 4 = (x - 2)/ 3

(11 + 1) / 4 = (11 - 2)/ 3

(12) / 4 = (9)/ 3

3 = 3

Hence verified.

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