Question

Solve 5x/2 - 2(2x-7) = 2(3x-1)

Answer 1

Answer:

32/15

Step-by-step explanation:

As per the provided information in the given question, we have a linear equation that is ;

• $\sf \dfrac{5x}{2} - 2(2x - 7) = 2(3x - 1)$

We've to calculate the value of x. Here, we'll be using the transposition method to solve this equation. In transposition method, we transpose the values form LHS to RHS. While transposing the values, we change their arithmetic operators. For example, if – 2 is getting transposed from LHS to RHS, so in RHS its arithmetic operator will be + 2.

Coming back to the question, we have :

$\twoheadrightarrow \sf{\quad { \dfrac{5x}{2} - 2(2x - 7) = 2(3x - 1) }}$

Firstly, we'll perform multiplication on both sides using distributive property.

$\twoheadrightarrow \sf{\quad { \dfrac{5x}{2} - 4x + 14 = 6x - 2 }}$

Now, transposing – 4x and + 14 from LHS to RHS. Their signs will get changed.

$\twoheadrightarrow \sf{\quad { \dfrac{5x}{2}= 6x - 2 + 4x - 14 }}$

Performing addition and subtraction of like terms in RHS. Here, 6x and 4x ; – 2 and – 14 are like terms.

$\twoheadrightarrow \sf{\quad { \dfrac{5x}{2}= 10x - 16 }}$

Now, transposing 2 from LHS to RHS. Its arithmetic operator will get changed. In LHS, it is in the form of division. In LHS, it will be in the form of multiplication.

$\twoheadrightarrow \sf{\quad { 5x=2( 10x - 16 )}}$

Performing multiplication in RHS using distributive property of multiplication over addition.

$\twoheadrightarrow \sf{\quad { 5x= 20x - 32}}$

Transposing 20x from LHS to RHS. Its sign will get changed.

$\twoheadrightarrow \sf{\quad { 5x - 20x = - 32}}$

Performing subtraction of terms in LHS.

$\twoheadrightarrow \sf{\quad { - 15x =- 32}}$

Transposing –15 from LHS to RHS. Its arithmetic operator will get changed. In LHS, it is in the form of multiplication. In LHS, it will be in the form of division.

$\twoheadrightarrow \sf{\quad { x = \cancel{\dfrac{- 32}{-15}} }}$

Now, cancelling the terms. Negative sign will get cancelled.

$\twoheadrightarrow \quad\underline{\boxed{ \pmb{\frak{ x}} =\dfrac{ \pmb{\frak{ 32}}}{\pmb{\frak{ 15}}} }}$

❝ Therefore, the value of x is 32/15. ❞

Answer 2

Step-by-step explanation:

5x/2 -2(2x−7)=2(3x−1)

5x/2 −4x+14=6x−2

5x/2=6x−2+4x−14

5x/2=10x-16

5x=2(10x−16)

5x=20x−32

-15x=−32

x=32/15

is required answer