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# Linear Equations in One Variable

Solve and check the following linear equations:

1. 6x -3 = 63

2. 5x - (2x - 10) = 35

3. 3x + 5 = 2x + 13

4. 3x + 14 = 12x - 5

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

6. 2 - (7x + 5) = 13 - 3x

7. 5x - (2x + 2) = x + (3x - 5)

8. 45 - [4 - 2y - 4 (y + 7)] = -4 (1 + 3y - [4 - 3 (y + 2) - 2 (2y - 5)]

#### Solution Preview

1) 6x -3 = 63
Or, 6x = 63+3 (Taking the constant 3 to the other side of the equation, and thus changing the sign.)
Or, 6x = 66
Or, x = 66/6 = 11

Check: Putting x= 11, in 6x -3 = 63, L.H.S. = 6 *11 - 3 = 66-3 = 63 = R.H.S.
Since, L.H.S. = R.H.S., therefore the answer is correct.

2) 5x - ( 2x - 10) = 35
Or, 5x -2x +10 = 35 (Removing the bracket)
Or, 5x – 2x = 35 – 10 (Taking the variables to one side and constants to the other side of the equation)
Or, 3x = 25
Or, x = 25/3

Check: Putting x= 25/3, in 5x - ( 2x - 10) = 35, L.H.S. = 5 *25/3 –{( 2*25/3) – 10)} = 35 = R.H.S.
Since, L.H.S. = R.H.S., therefore the answer is correct.

3) 3x + 5 = 2x + 13
...

#### Solution Summary

This solution is comprised of a detailed step-by-step calculation of the given Linear Equations. This solution provides students with a clear perspective of solving linear equations in Algebra.

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