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Solve the following linear equations for the variable: 2x + 1 = 7x + 3 8 − 3x = 2x − 5 5(a − 1) = 3(2a + 1) 2(x + 5) = 4 − x 4(3 - 5y) = -7(5 - 4y)

Mathematics

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Here are the solutions to the assignment problems:

1)

  1. Write the given equation.

    2x+1=7x+32x + 1 = 7x + 3

  2. Subtract $2x$ from both sides.

    1=5x+31 = 5x + 3

  3. Subtract 3 from both sides.

    −2=5x-2 = 5x

  4. Divide by 5.

    x=−25x = -\frac{2}{5}

    The solution is

    x=−25\boxed{x = -\frac{2}{5}}

    2)

  5. Write the given equation.

    8−3x=2x−58 - 3x = 2x - 5

  6. Add $3x$ to both sides.

    8=5x−58 = 5x - 5

  7. Add 5 to both sides.

    13=5x13 = 5x

  8. Divide by 5.

    x=135x = \frac{13}{5}

    The solution is

    x=135\boxed{x = \frac{13}{5}}

    3)

  9. Write the given equation.

    5(a−1)=3(2a+1)5(a - 1) = 3(2a + 1)

  10. Distribute the numbers on both sides.

    5a−5=6a+35a - 5 = 6a + 3

  11. Subtract $5a$ from both sides.

    −5=a+3-5 = a + 3

  12. Subtract 3 from both sides.

    −8=a-8 = a

    The solution is

    a=−8\boxed{a = -8}

    4)

  13. Write the given equation.

    2(x+5)=4−x2(x + 5) = 4 - x

  14. Distribute the 2 on the left side.

    2x+10=4−x2x + 10 = 4 - x

  15. Add xx to both sides.

    3x+10=43x + 10 = 4

  16. Subtract 10 from both sides.

    3x=−63x = -6

  17. Divide by 3.

    x=−2x = -2

    The solution is

    x=−2\boxed{x = -2}

    5)

  18. Write the given equation.

    4(3−5y)=−7(5−4y)4(3 - 5y) = -7(5 - 4y)

  19. Distribute the numbers on both sides.

    12−20y=−35+28y12 - 20y = -35 + 28y

  20. Add $20y$ to both sides.

    12=−35+48y12 = -35 + 48y

  21. Add 35 to both sides.

    47=48y47 = 48y

  22. Divide by 48.

    y=4748y = \frac{47}{48}

    The solution is

    y=4748\boxed{y = \frac{47}{48}}
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