Solve (k-8/7) - (-7/5k 7/4)

Question

Simplify the expression

\frac{69}{20} k - \frac{8}{7}

Evaluate

(k - \frac{8}{7}) - (- \frac{7}{5} k \times \frac{7}{4})

Remove the parentheses

k - \frac{8}{7} - (- \frac{7}{5} k \times \frac{7}{4})

Multiply the terms

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Multiply the terms

- \frac{7}{5} k \times \frac{7}{4}

Multiply the terms

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Evaluate

\frac{7}{5} \times \frac{7}{4}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7 \times 7}{5 \times 4}

Multiply the numbers

\frac{49}{5 \times 4}

Multiply the numbers

\frac{49}{20}

- \frac{49}{20} k

k - \frac{8}{7} - (- \frac{49}{20} k)

Rewrite the expression

k - \frac{8}{7} + \frac{49}{20} k

Solution

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Evaluate

k + \frac{49}{20} k

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

(1 + \frac{49}{20}) k

Add the numbers

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Evaluate

1 + \frac{49}{20}

Reduce fractions to a common denominator

\frac{20}{20} + \frac{49}{20}

Write all numerators above the common denominator

\frac{20 + 49}{20}

Add the numbers

\frac{69}{20}

\frac{69}{20} k

\frac{69}{20} k - \frac{8}{7}

Show Solution

Factor the expression

\frac{1}{140} (483 k - 160)

Evaluate

(k - \frac{8}{7}) - (- \frac{7}{5} k \times \frac{7}{4})

Remove the parentheses

k - \frac{8}{7} - (- \frac{7}{5} k \times \frac{7}{4})

Multiply the terms

More Steps

Multiply the terms

\frac{7}{5} k \times \frac{7}{4}

Multiply the terms

More Steps

Evaluate

\frac{7}{5} \times \frac{7}{4}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7 \times 7}{5 \times 4}

Multiply the numbers

\frac{49}{5 \times 4}

Multiply the numbers

\frac{49}{20}

\frac{49}{20} k

k - \frac{8}{7} - (- \frac{49}{20} k)

Rewrite the expression

k - \frac{8}{7} + \frac{49}{20} k

Add the terms

More Steps

Evaluate

k + \frac{49}{20} k

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

(1 + \frac{49}{20}) k

Add the numbers

More Steps

Evaluate

1 + \frac{49}{20}

Reduce fractions to a common denominator

\frac{20}{20} + \frac{49}{20}

Write all numerators above the common denominator

\frac{20 + 49}{20}

Add the numbers

\frac{69}{20}

\frac{69}{20} k

\frac{69}{20} k - \frac{8}{7}

Solution

\frac{1}{140} (483 k - 160)

Show Solution

Find the roots

k = \frac{160}{483}

Alternative Form

k \approx 0.331263

Evaluate

(k - \frac{8}{7}) - (- \frac{7}{5} k \times \frac{7}{4})

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

(k - \frac{8}{7}) - (- \frac{7}{5} k \times \frac{7}{4}) = 0

Remove the parentheses

k - \frac{8}{7} - (- \frac{7}{5} k \times \frac{7}{4}) = 0

Multiply the terms

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Multiply the terms

\frac{7}{5} k \times \frac{7}{4}

Multiply the terms

More Steps

Evaluate

\frac{7}{5} \times \frac{7}{4}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7 \times 7}{5 \times 4}

Multiply the numbers

\frac{49}{5 \times 4}

Multiply the numbers

\frac{49}{20}

\frac{49}{20} k

k - \frac{8}{7} - (- \frac{49}{20} k) = 0

Subtract the terms

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Simplify

k - \frac{8}{7} - (- \frac{49}{20} k)

Rewrite the expression

k - \frac{8}{7} + \frac{49}{20} k

Add the terms

More Steps

Evaluate

k + \frac{49}{20} k

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

(1 + \frac{49}{20}) k

Add the numbers

\frac{69}{20} k

\frac{69}{20} k - \frac{8}{7}

\frac{69}{20} k - \frac{8}{7} = 0

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

\frac{69}{20} k = 0 + \frac{8}{7}

Add the terms

\frac{69}{20} k = \frac{8}{7}

Multiply by the reciprocal

\frac{69}{20} k \times \frac{20}{69} = \frac{8}{7} \times \frac{20}{69}

Multiply

k = \frac{8}{7} \times \frac{20}{69}

Solution

More Steps

Evaluate

\frac{8}{7} \times \frac{20}{69}

To multiply the fractions,multiply the numerators and denominators separately

\frac{8 \times 20}{7 \times 69}

Multiply the numbers

\frac{160}{7 \times 69}

Multiply the numbers

\frac{160}{483}

k = \frac{160}{483}

Alternative Form

k \approx 0.331263

Show Solution