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Exercise - 2.3

Linear Equations in One Variable

**Question-1 :-** Solve the equation and check result 3x = 2x + 18 .

3x = 2x + 18 3x - 2x = 18 x = 18 Verification : L.H.S = 3x = 3 x 18 = 54 R.H.S = 2x + 18 = 2 x 18 + 18 = 36 + 18 = 54 L.H.S = R.H.S

**Question-2 :-** Solve the equation and check result 5t – 3 = 3t – 5 .

5t – 3 = 3t – 5 5t - 3t = -5 + 3 2t = -2 t = -2/2 t = -1 Verification : L.H.S = 5t – 3 = 5 x (-1) - 3 = -5 - 3 = -8 R.H.S = 3t – 5 = 3 x (-1) - 5 = -3 - 5 = -8 L.H.S = R.H.S

**Question-3 :-** Solve the equation and check result 5x + 9 = 5 + 3x .

5x + 9 = 5 + 3x 5x - 3x = 5 - 9 2x = -4 x = -4/2 x = -2 Verification : L.H.S = 5x + 9 = 5 x (-2) + 9 = -10 + 9 = -1 R.H.S = 5 + 3x = 5 + 3 x (-2) = 5 - 6 = -1 L.H.S = R.H.S

**Question-4 :-** Solve the equation and check result 4z + 3 = 6 + 2z .

4z + 3 = 6 + 2z 4z - 2z = 6 - 3 2z = 3 z = 3/2 Verification : L.H.S = 4z + 3 = 4 x 3/2 + 3 = 2 x 3 + 3 = 6 + 3 = 9 R.H.S = 6 + 2z = 6 + 2 x 3/2 = 6 + 3 = 9 L.H.S = R.H.S

**Question-5 :-** Solve the equation and check result 2x – 1 = 14 – x .

2x – 1 = 14 – x 2x + x = 14 + 1 3x = 15 x = 15/3 x = 5 Verification : L.H.S = 2x - 1 = 2 x 5 - 1 = 10 - 1 = 9 R.H.S = 14 - x = 14 - 5 = 9 L.H.S = R.H.S

**Question-6 :-** Solve the equation and check result 8x + 4 = 3 (x – 1) + 7 .

8x + 4 = 3 (x – 1) + 7 8x + 4 = 3x - 3 + 7 8x - 3x = 4 - 4 5x = 0 x = 0/5 x = 0 Verification : L.H.S = 8x + 4 = 8 x 0 + 4 = 0 + 4 = 4 R.H.S = 3 (x – 1) + 7 = 3 (0 - 1) + 7 = -3 + 7 = 4 L.H.S = R.H.S

**Question-7 :-** Solve the equation and check result x = 4/5 (x + 10) .

x = 4/5 (x + 10) x = 4x/5 + 10 x 4/5 x - 4x/5 = 2 x 4 (5x - 4x)/5 = 8 x/5 = 8 x = 8 x 5 x = 40 Verification : L.H.S = x = 40 R.H.S = 4/5 (x + 10) = 4/5 (40 + 10) = 4/5 x 50 = 4 x 10 = 40 L.H.S = R.H.S

**Question-8 :-** Solve the equation and check result 2x/3 + 1 = 7x/15 + 3 .

2x/3 + 1 = 7x/15 + 3 2x/3 - 7x/15 = 3 - 1 (10x - 7x)/15 = 2 3x/15 = 2 x/5 = 2 x = 10 Verification : L.H.S = 2x/3 + 1 = (2 x 10)/3 + 1 = 20/3 + 1 = (20 + 3)/3 = 23/3 R.H.S = 7x/15 + 3 = (7 x 10)/15 + 3 = 70/15 + 3 = 14/3 + 3 = (14 + 9)/3 = 23/3 L.H.S = R.H.S

**Question-9 :-** Solve the equation and check result 2y + 5/3 = 26/3 – y .

2y + 5/3 = 26/3 – y 2y + y = 26/3 - 5/3 3y = (26 - 5)/3 3y = 21/3 3y = 7 y = 7/3 Verification : L.H.S = 2y + 5/3 = (2 x 7/3) + 5/3 = 14/3 + 5/3 = (14 + 5)/3 = 19/3 R.H.S = 26/3 – y = 26/3 - 7/3 = (26 - 7)/3 = 19/3 L.H.S = R.H.S

**Question-10 :-** Solve the equation and check result 3m = 5 m – 8/5 .

3m = 5m – 8/5 8/5 = 5m - 3m 8/5 = 2m 2m = 8/5 m = 8/(5 x 2) m = 4/5 Verification : L.H.S = 3m = 3 x 4/5 = 12/5 R.H.S = 5m – 8/5 = 5 x 4/5 - 8/5 = 4 - 8/5 = (20 - 8)/5 = 12/5 L.H.S = R.H.S

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