Solve 3 2/3 x- 4/5 (x-3 3/4 )

Question

Simplify the expression

\frac{43}{15} x + 3

Evaluate

3 \frac{2}{3} \times x - \frac{4}{5} (x - 3 \frac{3}{4})

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{3}{4}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{3 \times 4 + 3}{4}

Multiply the terms

\frac{12 + 3}{4}

Add the terms

\frac{15}{4}

3 \frac{2}{3} \times x - \frac{4}{5} (x - \frac{15}{4})

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{2}{3}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

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

Multiply the terms

\frac{9 + 2}{3}

Add the terms

\frac{11}{3}

\frac{11}{3} x - \frac{4}{5} (x - \frac{15}{4})

Multiply the terms

More Steps

Evaluate

\frac{4}{5} (x - \frac{15}{4})

Apply the distributive property

\frac{4}{5} x - \frac{4}{5} \times \frac{15}{4}

Multiply the numbers

More Steps

Evaluate

\frac{4}{5} \times \frac{15}{4}

Reduce the numbers

\frac{1}{5} \times 15

Reduce the numbers

1 \times 3

Simplify

3

\frac{4}{5} x - 3

\frac{11}{3} x - (\frac{4}{5} x - 3)

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

\frac{11}{3} x - \frac{4}{5} x + 3

Solution

More Steps

Evaluate

\frac{11}{3} x - \frac{4}{5} x

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

(\frac{11}{3} - \frac{4}{5}) x

Subtract the numbers

More Steps

Evaluate

\frac{11}{3} - \frac{4}{5}

Reduce fractions to a common denominator

\frac{11 \times 5}{3 \times 5} - \frac{4 \times 3}{5 \times 3}

Multiply the numbers

\frac{11 \times 5}{15} - \frac{4 \times 3}{5 \times 3}

Multiply the numbers

\frac{11 \times 5}{15} - \frac{4 \times 3}{15}

Write all numerators above the common denominator

\frac{11 \times 5 - 4 \times 3}{15}

Multiply the numbers

\frac{55 - 4 \times 3}{15}

Multiply the numbers

\frac{55 - 12}{15}

Subtract the numbers

\frac{43}{15}

\frac{43}{15} x

\frac{43}{15} x + 3

Show Solution

Factor the expression

\frac{1}{15} (43 x + 45)

Evaluate

3 \frac{2}{3} \times x - \frac{4}{5} (x - 3 \frac{3}{4})

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{3}{4}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{3 \times 4 + 3}{4}

Multiply the terms

\frac{12 + 3}{4}

Add the terms

\frac{15}{4}

3 \frac{2}{3} \times x - \frac{4}{5} (x - \frac{15}{4})

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{2}{3}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

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

Multiply the terms

\frac{9 + 2}{3}

Add the terms

\frac{11}{3}

\frac{11}{3} x - \frac{4}{5} (x - \frac{15}{4})

Simplify

More Steps

Evaluate

- \frac{4}{5} (x - \frac{15}{4})

Apply the distributive property

- \frac{4}{5} x - \frac{4}{5} (- \frac{15}{4})

Multiply the terms

More Steps

Evaluate

- \frac{4}{5} (- \frac{15}{4})

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

\frac{4}{5} \times \frac{15}{4}

Reduce the numbers

\frac{1}{5} \times 15

Reduce the numbers

1 \times 3

Simplify

3

- \frac{4}{5} x + 3

\frac{11}{3} x - \frac{4}{5} x + 3

Subtract the terms

More Steps

Evaluate

\frac{11}{3} x - \frac{4}{5} x

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

(\frac{11}{3} - \frac{4}{5}) x

Subtract the numbers

More Steps

Evaluate

\frac{11}{3} - \frac{4}{5}

Reduce fractions to a common denominator

\frac{11 \times 5}{3 \times 5} - \frac{4 \times 3}{5 \times 3}

Multiply the numbers

\frac{11 \times 5}{15} - \frac{4 \times 3}{5 \times 3}

Multiply the numbers

\frac{11 \times 5}{15} - \frac{4 \times 3}{15}

Write all numerators above the common denominator

\frac{11 \times 5 - 4 \times 3}{15}

Multiply the numbers

\frac{55 - 4 \times 3}{15}

Multiply the numbers

\frac{55 - 12}{15}

Subtract the numbers

\frac{43}{15}

\frac{43}{15} x

\frac{43}{15} x + 3

Solution

\frac{1}{15} (43 x + 45)

Show Solution

Find the roots

x = - \frac{45}{43}

Alternative Form

x \approx - 1.046512

Evaluate

3 \frac{2}{3} \times x - \frac{4}{5} (x - 3 \frac{3}{4})

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

3 \frac{2}{3} \times x - \frac{4}{5} (x - 3 \frac{3}{4}) = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{3}{4}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{3 \times 4 + 3}{4}

Multiply the terms

\frac{12 + 3}{4}

Add the terms

\frac{15}{4}

3 \frac{2}{3} \times x - \frac{4}{5} (x - \frac{15}{4}) = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

3 \frac{2}{3}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

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

Multiply the terms

\frac{9 + 2}{3}

Add the terms

\frac{11}{3}

\frac{11}{3} x - \frac{4}{5} (x - \frac{15}{4}) = 0

Multiply the terms

More Steps

Evaluate

\frac{4}{5} (x - \frac{15}{4})

Apply the distributive property

\frac{4}{5} x - \frac{4}{5} \times \frac{15}{4}

Multiply the numbers

More Steps

Evaluate

\frac{4}{5} \times \frac{15}{4}

Reduce the numbers

\frac{1}{5} \times 15

Reduce the numbers

1 \times 3

Simplify

3

\frac{4}{5} x - 3

\frac{11}{3} x - (\frac{4}{5} x - 3) = 0

Subtract the terms

More Steps

Simplify

\frac{11}{3} x - (\frac{4}{5} x - 3)

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

\frac{11}{3} x - \frac{4}{5} x + 3

Subtract the terms

More Steps

Evaluate

\frac{11}{3} x - \frac{4}{5} x

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

(\frac{11}{3} - \frac{4}{5}) x

Subtract the numbers

\frac{43}{15} x

\frac{43}{15} x + 3

\frac{43}{15} x + 3 = 0

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

\frac{43}{15} x = 0 - 3

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

\frac{43}{15} x = - 3

Multiply by the reciprocal

\frac{43}{15} x \times \frac{15}{43} = - 3 \times \frac{15}{43}

Multiply

x = - 3 \times \frac{15}{43}

Solution

More Steps

Evaluate

- 3 \times \frac{15}{43}

Multiply the numbers

- \frac{3 \times 15}{43}

Multiply the numbers

- \frac{45}{43}

x = - \frac{45}{43}

Alternative Form

x \approx - 1.046512

Show Solution