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Solve the following linear equations: 1. 5x + 9 = 5 + 3x 2. 8x + 4 = 3(x − 1) + 7 3. 2y + 5/3 = 26/3 - y

Mathematics

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प्रश्न 3:

5x+9=5+3x5x + 9 = 5 + 3x
  1. Subtract $3x$ from both sides.

    5x−3x+9=55x - 3x + 9 = 5 2x+9=52x + 9 = 5
  2. Subtract 9 from both sides.

    2x=5−92x = 5 - 9 2x=−42x = -4
  3. Divide by 2.

    x=−42x = \frac{-4}{2} x=−2x = -2

    The solution is x=−2\boxed{x = -2}.

    प्रश्न 6:

    8x+4=3(x−1)+78x + 4 = 3(x - 1) + 7
  4. Distribute the 3 on the right side.

    8x+4=3x−3+78x + 4 = 3x - 3 + 7 8x+4=3x+48x + 4 = 3x + 4
  5. Subtract $3x$ from both sides.

    8x−3x+4=48x - 3x + 4 = 4 5x+4=45x + 4 = 4
  6. Subtract 4 from both sides.

    5x=4−45x = 4 - 4 5x=05x = 0
  7. Divide by 5.

    x=05x = \frac{0}{5} x=0x = 0

    The solution is x=0\boxed{x = 0}.

    प्रश्न 9:

    2y+53=263−y2y + \frac{5}{3} = \frac{26}{3} - y
  8. Add yy to both sides.

    2y+y+53=2632y + y + \frac{5}{3} = \frac{26}{3} 3y+53=2633y + \frac{5}{3} = \frac{26}{3}
  9. Subtract 53\frac{5}{3} from both sides.

    3y=263−533y = \frac{26}{3} - \frac{5}{3} 3y=26−533y = \frac{26 - 5}{3} 3y=2133y = \frac{21}{3} 3y=73y = 7
  10. Divide by 3.

    y=73y = \frac{7}{3}

    The solution is y=73\boxed{y = \frac{7}{3}}.

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