Question

Solve the following using the transposition method.
a. 5(x-2) + 4( x+1) = 3(x+5)

Answer 1

Answer:

x = 7/2

Step-by-step explanation:

5(x-2) + 4(x+1) = 3(x+5)

5x - 10 + 4x + 4 = 3x + 15

5x + 4x - 3x = 15 + 10 - 4

9x - 3x = 25 - 4

6x = 21

x = 21/6

x = 7/2

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Answer 2

GIVEN :-

$\\ \sf \: 5(x - 2) + 4(x + 1) = 3(x + 5)$

TO FIND :-

• Value of x.

SOLUTION :-

We have ,

$\\ \sf \: 5(x - 2) + 4(x + 1) = 3(x + 5)$

We know ,

p(a + b) = pa + pb

$\\ \sf \implies \: 5(x) - 5(2) + 4(x) + 4(1) = 3(x) + 3(5) \\ \\ \implies \sf \: 5x - 10 + 4x + 4 = 3x + 15$

Arranging like terms together ,

$\\ \implies \sf \: 5x + 4x - 10 + 4 = 3x + 15 \\ \\ \implies \sf \: 9x - 6 = 3x + 15$

Now , we will transpose 3x to left hand side . As 3x is in addition form in right hand side , it will be in subtraction form on left hand side.

Also , we will transpose 6 to right hand side . As 6 is in subtraction form on left hand side , it will be in addition form on Right hand side.

$\\ \implies \sf \: 9x - 3x = 15 + 6 \\ \\ \implies \sf \: 6x = 21$

Now we will transpose 6 to right hand side. As it is in multiplication form on left hand side , it will be in division form on Right hand side.

$\\ \implies \underline{\boxed{\sf \: x = \dfrac{21}{6} }}$

Hence , value of x is 21/6.

VERIFICATION :-

$\\ \implies \tt \: 5 \left( \dfrac{21}{6} - 2 \right) + 4 \left( \dfrac{21}{6} + 1 \right) = 3 \left( \dfrac{21}{6} + 5 \right) \\ \\ \\ \implies \tt \: 5\left( \dfrac{21 - 12}{6} \right) + 4\left( \dfrac{21 + 6}{6} \right) = 3\left( \dfrac{21 + 30}{6} \right) \\ \\ \\ \implies \tt \: 5\left( \dfrac{9}{6} \right) + 4\left( \dfrac{27}{6} \right) = 3\left( \dfrac{51}{6} \right) \\ \\ \\ \implies \tt \: \dfrac{45}{6} + \dfrac{108}{6} = \dfrac{153}{6} \\ \\ \\ \implies \tt \: \dfrac{153}{6} = \dfrac{153}{6} \: \: \: \: \: \: \: \: \: \: (verified)$