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Find a common denominator, which is 3 x 5 = 15.

Mathematics

ScanSolve AI Answer

Answer

−x−715\frac{-x-7}{15}

90

Step-by-step solution

9 steps

QUESTION ONE

  1. Express: x+13−2x+45\frac{x+1}{3} - \frac{2x+4}{5} as a single fraction in its simplest form.

  1. Find a common denominator, which is 3×5=153 \times 5 = 15.

    5(x+1)15−3(2x+4)15\frac{5(x+1)}{15} - \frac{3(2x+4)}{15}

  2. Combine the numerators over the common denominator.

    5(x+1)−3(2x+4)15\frac{5(x+1) - 3(2x+4)}{15}

  3. Expand the terms in the numerator.

    5x+5−(6x+12)15\frac{5x+5 - (6x+12)}{15}

  4. Distribute the negative sign and simplify the numerator.

    5x+5−6x−1215\frac{5x+5 - 6x - 12}{15} −x−715\frac{-x - 7}{15}

    The simplified expression is −x−715\boxed{\frac{-x-7}{15}}.

    1. Calculate the value of 0.45÷0.0050.45 \div 0.005.

  5. Convert the division to a fraction.

    0.450.005\frac{0.45}{0.005}

  6. Multiply the numerator and denominator by 1000 to remove the decimals.

    0.45×10000.005×1000=4505\frac{0.45 \times 1000}{0.005 \times 1000} = \frac{450}{5}

  7. Perform the division.

    4505=90\frac{450}{5} = 90

    The value is 90\boxed{90}.

    1. Make y the subject: p=2y−cmp = \frac{2y-c}{m}.

  8. Multiply both sides by mm.

    pm=2y−cpm = 2y-c

  9. Add cc to both

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