Solve -5h-3/2(3/2h-3)

Question

Simplify the expression

- \frac{29}{4} h + \frac{9}{2}

Evaluate

- 5 h - \frac{3}{2} (\frac{3}{2} h - 3)

Multiply the terms

More Steps

Evaluate

\frac{3}{2} (\frac{3}{2} h - 3)

Apply the distributive property

\frac{3}{2} \times \frac{3}{2} h - \frac{3}{2} \times 3

Multiply the numbers

More Steps

Evaluate

\frac{3}{2} \times \frac{3}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3 \times 3}{2 \times 2}

Multiply the numbers

\frac{9}{2 \times 2}

Multiply the numbers

\frac{9}{4}

\frac{9}{4} h - \frac{3}{2} \times 3

Multiply the numbers

More Steps

Evaluate

\frac{3}{2} \times 3

Multiply the numbers

\frac{3 \times 3}{2}

Multiply the numbers

\frac{9}{2}

\frac{9}{4} h - \frac{9}{2}

- 5 h - (\frac{9}{4} h - \frac{9}{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 5 h - \frac{9}{4} h + \frac{9}{2}

Solution

More Steps

Evaluate

- 5 h - \frac{9}{4} h

Collect like terms by calculating the sum or difference of their coefficients

(- 5 - \frac{9}{4}) h

Subtract the numbers

More Steps

Evaluate

- 5 - \frac{9}{4}

Reduce fractions to a common denominator

- \frac{5 \times 4}{4} - \frac{9}{4}

Write all numerators above the common denominator

\frac{- 5 \times 4 - 9}{4}

Multiply the numbers

\frac{- 20 - 9}{4}

Subtract the numbers

\frac{- 29}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{29}{4}

- \frac{29}{4} h

- \frac{29}{4} h + \frac{9}{2}

Show Solution

Factor the expression

\frac{1}{4} (- 29 h + 18)

Evaluate

- 5 h - \frac{3}{2} (\frac{3}{2} h - 3)

Simplify

More Steps

Evaluate

- \frac{3}{2} (\frac{3}{2} h - 3)

Apply the distributive property

- \frac{3}{2} \times \frac{3}{2} h - \frac{3}{2} (- 3)

Multiply the terms

More Steps

Evaluate

- \frac{3}{2} \times \frac{3}{2}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{3 \times 3}{2 \times 2}

Multiply the numbers

- \frac{9}{2 \times 2}

Multiply the numbers

- \frac{9}{4}

- \frac{9}{4} h - \frac{3}{2} (- 3)

Multiply the terms

More Steps

Evaluate

- \frac{3}{2} (- 3)

Multiplying or dividing an even number of negative terms equals a positive

\frac{3}{2} \times 3

Multiply the numbers

\frac{3 \times 3}{2}

Multiply the numbers

\frac{9}{2}

- \frac{9}{4} h + \frac{9}{2}

- 5 h - \frac{9}{4} h + \frac{9}{2}

Subtract the terms

More Steps

Evaluate

- 5 h - \frac{9}{4} h

Collect like terms by calculating the sum or difference of their coefficients

(- 5 - \frac{9}{4}) h

Subtract the numbers

More Steps

Evaluate

- 5 - \frac{9}{4}

Reduce fractions to a common denominator

- \frac{5 \times 4}{4} - \frac{9}{4}

Write all numerators above the common denominator

\frac{- 5 \times 4 - 9}{4}

Multiply the numbers

\frac{- 20 - 9}{4}

Subtract the numbers

\frac{- 29}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{29}{4}

- \frac{29}{4} h

- \frac{29}{4} h + \frac{9}{2}

Solution

\frac{1}{4} (- 29 h + 18)

Show Solution

Find the roots

h = \frac{18}{29}

Alternative Form

h \approx 0.62069

Evaluate

- 5 h - \frac{3}{2} (\frac{3}{2} h - 3)

To find the roots of the expression,set the expression equal to 0

- 5 h - \frac{3}{2} (\frac{3}{2} h - 3) = 0

Multiply the terms

More Steps

Evaluate

\frac{3}{2} (\frac{3}{2} h - 3)

Apply the distributive property

\frac{3}{2} \times \frac{3}{2} h - \frac{3}{2} \times 3

Multiply the numbers

More Steps

Evaluate

\frac{3}{2} \times \frac{3}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3 \times 3}{2 \times 2}

Multiply the numbers

\frac{9}{2 \times 2}

Multiply the numbers

\frac{9}{4}

\frac{9}{4} h - \frac{3}{2} \times 3

Multiply the numbers

More Steps

Evaluate

\frac{3}{2} \times 3

Multiply the numbers

\frac{3 \times 3}{2}

Multiply the numbers

\frac{9}{2}

\frac{9}{4} h - \frac{9}{2}

- 5 h - (\frac{9}{4} h - \frac{9}{2}) = 0

Subtract the terms

More Steps

Simplify

- 5 h - (\frac{9}{4} h - \frac{9}{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 5 h - \frac{9}{4} h + \frac{9}{2}

Subtract the terms

More Steps

Evaluate

- 5 h - \frac{9}{4} h

Collect like terms by calculating the sum or difference of their coefficients

(- 5 - \frac{9}{4}) h

Subtract the numbers

- \frac{29}{4} h

- \frac{29}{4} h + \frac{9}{2}

- \frac{29}{4} h + \frac{9}{2} = 0

Move the constant to the right-hand side and change its sign

- \frac{29}{4} h = 0 - \frac{9}{2}

Removing 0 doesn't change the value,so remove it from the expression

- \frac{29}{4} h = - \frac{9}{2}

Change the signs on both sides of the equation

\frac{29}{4} h = \frac{9}{2}

Multiply by the reciprocal

\frac{29}{4} h \times \frac{4}{29} = \frac{9}{2} \times \frac{4}{29}

Multiply

h = \frac{9}{2} \times \frac{4}{29}

Solution

More Steps

Evaluate

\frac{9}{2} \times \frac{4}{29}

Reduce the numbers

9 \times \frac{2}{29}

Multiply the numbers

\frac{9 \times 2}{29}

Multiply the numbers

\frac{18}{29}

h = \frac{18}{29}

Alternative Form

h \approx 0.62069

Show Solution