Solve (x-1 2/3)-4(3-x)=-3x

Question

Solve the equation

x = \frac{41}{24}

Alternative Form

x = 1.708 \dot{3}

Evaluate

(x - 1 \frac{2}{3}) - 4 (3 - x) = - 3 x

Simplify

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Evaluate

(x - 1 \frac{2}{3}) - 4 (3 - x)

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

1 \frac{2}{3}

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

\frac{3 + 2}{3}

Add the terms

\frac{5}{3}

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

Remove the parentheses

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

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

Move the expression to the left side

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

Subtract the terms

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Evaluate

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

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

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

Add the terms

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Evaluate

x + 3 x

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

(1 + 3) x

Add the numbers

4 x

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

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

Calculate

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Evaluate

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

Expand the expression

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Calculate

- 4 (3 - x)

Apply the distributive property

- 4 \times 3 - (- 4 x)

Multiply the numbers

- 12 - (- 4 x)

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

- 12 + 4 x

4 x - \frac{5}{3} - 12 + 4 x

Add the terms

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Evaluate

4 x + 4 x

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

(4 + 4) x

Add the numbers

8 x

8 x - \frac{5}{3} - 12

Subtract the numbers

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Evaluate

- \frac{5}{3} - 12

Reduce fractions to a common denominator

- \frac{5}{3} - \frac{12 \times 3}{3}

Write all numerators above the common denominator

\frac{- 5 - 12 \times 3}{3}

Multiply the numbers

\frac{- 5 - 36}{3}

Subtract the numbers

\frac{- 41}{3}

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

- \frac{41}{3}

8 x - \frac{41}{3}

8 x - \frac{41}{3} = 0

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

8 x = 0 + \frac{41}{3}

Add the terms

8 x = \frac{41}{3}

Multiply by the reciprocal

8 x \times \frac{1}{8} = \frac{41}{3} \times \frac{1}{8}

Multiply

x = \frac{41}{3} \times \frac{1}{8}

Solution

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Evaluate

\frac{41}{3} \times \frac{1}{8}

To multiply the fractions,multiply the numerators and denominators separately

\frac{41}{3 \times 8}

Multiply the numbers

\frac{41}{24}

x = \frac{41}{24}

Alternative Form

x = 1.708 \dot{3}

Show Solution

Rewrite the equation

24 x = 41

Evaluate

(x - 1 \frac{2}{3}) - 4 (3 - x) = - 3 x

Evaluate

More Steps

Evaluate

(x - 1 \frac{2}{3}) - 4 (3 - x)

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

1 \frac{2}{3}

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

\frac{3 + 2}{3}

Add the terms

\frac{5}{3}

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

Remove the parentheses

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

Expand the expression

More Steps

Calculate

- 4 (3 - x)

Apply the distributive property

- 4 \times 3 - (- 4 x)

Multiply the numbers

- 12 - (- 4 x)

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

- 12 + 4 x

x - \frac{5}{3} - 12 + 4 x

Add the terms

More Steps

Evaluate

x + 4 x

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

(1 + 4) x

Add the numbers

5 x

5 x - \frac{5}{3} - 12

Subtract the numbers

More Steps

Evaluate

- \frac{5}{3} - 12

Reduce fractions to a common denominator

- \frac{5}{3} - \frac{12 \times 3}{3}

Write all numerators above the common denominator

\frac{- 5 - 12 \times 3}{3}

Multiply the numbers

\frac{- 5 - 36}{3}

Subtract the numbers

\frac{- 41}{3}

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

- \frac{41}{3}

5 x - \frac{41}{3}

5 x - \frac{41}{3} = - 3 x

Multiply both sides of the equation by LCD

15 x - 41 = - 9 x

Move the variable to the left side

24 x - 41 = 0

Solution

24 x = 41

Show Solution

Solve the equation

Rewrite the equation

Graph