Answer:
- x = 3/4
- Therefore , option A is correct .
Explanation:
In the question we're given with an equation i.e.,
- 2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4
And we are asked to find the value of x .
Solution :
![\longmapsto \: 2 ( 6 - 2x ) - 2x = 2 ( 5 + x ) - 4](https://img.qammunity.org/2023/formulas/mathematics/high-school/cci8v3vqcykx1pbx7jbm4kcqqi9wmo24mo.png)
Step 1 : Solving parenthesis by multiplying it with 2 on both the sides :
![\longmapsto \: 12 - \bold{4x} - \bold{2x} = \bold{10} + 2x - \bold{4}](https://img.qammunity.org/2023/formulas/mathematics/high-school/olodt2qcbwtmup17h392ppgr8n06jakg48.png)
Step 2 : Adding like terms on left hand side and subtracting like terms on right hand side :
![\longmapsto \: 12 - 6x = 2x + 6](https://img.qammunity.org/2023/formulas/mathematics/high-school/6k4r5y8xbeov1ge0ilt9tawothqy968ii3.png)
Step 3 : Transposing 12 to right hand side and 2x to left hand side :
![\longmapsto \: -2x - 6x = 6 - 12](https://img.qammunity.org/2023/formulas/mathematics/high-school/p37v0tlw8d1t8acgr24uv9c3ucpncrrfbo.png)
On further calculations we get :
![\longmapsto \: \cancel{ - }8x = \cancel{- }6](https://img.qammunity.org/2023/formulas/mathematics/high-school/az4p4ow0w4y1w2a0527u639q6awxscaqa6.png)
Step 4 : Transposing 8 to right hand side :
![\longmapsto \: x = \frac{\cancel{6}}{\cancel{8}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/nzkviinjr49tvndea9y8gevp4saoo1o4f0.png)
Step 5 : Cancelling 6/8 to their simplest form :
![\longmapsto \: \pink{\boxed{x = (3)/(4) }}](https://img.qammunity.org/2023/formulas/mathematics/high-school/4az7brkw7hoetb5fqucm717vre0qgdbh5f.png)
- Therefore , value of x is 3/4 and it will make the equation true .
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