CBSE Class 7 Mathematics Simple Equations Assignment Set 05

Question. Solve the following system of equations for \(x\): \(x - 7 = 5 + \frac{x}{2}\)
Answer:
Subtracting \(\frac{x}{2}\) from both sides and adding \(7\) to both sides:
\(x - \frac{x}{2} = 5 + 7\)
\(\frac{x}{2} = 12\)
Multiplying by 2:
\(x = 24\)

Question. \(3(x + 3) - 2(x - 1) = 5(x - 5)\)
Answer:
Expanding the terms:
\(3x + 9 - 2x + 2 = 5x - 25\)
Simplifying the left-hand side:
\(x + 11 = 5x - 25\)
Rearranging terms:
\(11 + 25 = 5x - x\)
\(36 = 4x\)
\(x = 9\)

Question. \(\frac{x}{8} - \frac{1}{2} = \frac{x}{6} - 2\)
Answer:
Multiplying the entire equation by the LCM of denominators (24):
\(3x - 12 = 4x - 48\)
Rearranging terms:
\(48 - 12 = 4x - 3x\)
\(x = 36\)

Question. \(3(x + 2) - 2(x - 1) = 7\)
Answer:
Expanding the terms:
\(3x + 6 - 2x + 2 = 7\)
Simplifying:
\(x + 8 = 7\)
\(x = 7 - 8\)
\(x = -1\)

Question. \(5(x - 1) + 2(x + 3) + 6 = 0\)
Answer:
Expanding the terms:
\(5x - 5 + 2x + 6 + 6 = 0\)
Simplifying:
\(7x + 7 = 0\)
\(7x = -7\)
\(x = -1\)

Question. \(6(1 - 4x) + 7(2 + 5x) = 53\)
Answer:
Expanding the terms:
\(6 - 24x + 14 + 35x = 53\)
Simplifying:
\(11x + 20 = 53\)
\(11x = 33\)
\(x = 3\)

Question. \(3(x + 6) + 2(x + 3) = 64\)
Answer:
Expanding the terms:
\(3x + 18 + 2x + 6 = 64\)
Simplifying:
\(5x + 24 = 64\)
\(5x = 40\)
\(x = 8\)

Question. \(3(2 - 5x) - 2(1 - 6x) = 1\)
Answer:
Expanding the terms:
\(6 - 15x - 2 + 12x = 1\)
Simplifying:
\(4 - 3x = 1\)
\(4 - 1 = 3x\)
\(3x = 3\)
\(x = 1\)

Question. \(\frac{x - 3}{5} - 2 = \frac{2x}{5}\)
Answer:
Multiplying the entire equation by 5:
\(x - 3 - 10 = 2x\)
\(x - 13 = 2x\)
\(-13 = 2x - x\)
\(x = -13\)

Question. \(\frac{2x}{5} - \frac{3}{2} = \frac{x}{2} + 1\)
Answer:
Multiplying the entire equation by the LCM of denominators (10):
\(4x - 15 = 5x + 10\)
Rearranging terms:
\(-15 - 10 = 5x - 4x\)
\(x = -25\)