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Solve the following linear equations: 1) 3x = 2x + 18, 2) 5t − 3 = 3t − 5, 4) 4z + 3 = 6 + 2z, 5) 2x − 1 = 14 − x

Mathematics

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प्रश्न 1:

3x=2x+183x = 2x + 18
  1. Subtract $2x$ from both sides.

    3x−2x=183x - 2x = 18 x=18x = 18

    The solution is x=18\boxed{x = 18}.

    प्रश्न 2:

    5t−3=3t−55t - 3 = 3t - 5
  2. Subtract $3t$ from both sides.

    5t−3t−3=−55t - 3t - 3 = -5 2t−3=−52t - 3 = -5
  3. Add 3 to both sides.

    2t=−5+32t = -5 + 3 2t=−22t = -2
  4. Divide by 2.

    t=−22t = \frac{-2}{2} t=−1t = -1

    The solution is t=−1\boxed{t = -1}.

    प्रश्न 4:

    4z+3=6+2z4z + 3 = 6 + 2z
  5. Subtract $2z$ from both sides.

    4z−2z+3=64z - 2z + 3 = 6 2z+3=62z + 3 = 6
  6. Subtract 3 from both sides.

    2z=6−32z = 6 - 3 2z=32z = 3
  7. Divide by 2.

    z=32z = \frac{3}{2}

    The solution is z=32\boxed{z = \frac{3}{2}}.

    प्रश्न 5:

    2x−1=14−x2x - 1 = 14 - x
  8. Add xx to both sides.

    2x+x−1=142x + x - 1 = 14 3x−1=143x - 1 = 14
  9. Add 1 to both sides.

    3x=14+13x = 14 + 1 3x=153x = 15
  10. Divide by 3.

    x=153x = \frac{15}{3} x=5x = 5

    The solution is x=5\boxed{x = 5}.

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