Solve 6r-37=7r-4(3-r)

Question

Solve the equation

r = - 5

Evaluate

6 r - 37 = 7 r - 4 (3 - r)

Move the expression to the left side

6 r - 37 - (7 r - 4 (3 - r)) = 0

Subtract the terms

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Evaluate

6 r - 37 - (7 r - 4 (3 - r))

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

6 r - 37 - 7 r + 4 (3 - r)

Subtract the terms

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Evaluate

6 r - 7 r

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

(6 - 7) r

Subtract the numbers

- r

- r - 37 + 4 (3 - r)

- r - 37 + 4 (3 - r) = 0

Calculate the sum or difference

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Evaluate

- r - 37 + 4 (3 - r)

Expand the expression

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Calculate

4 (3 - r)

Apply the distributive property

4 \times 3 - 4 r

Multiply the numbers

12 - 4 r

- r - 37 + 12 - 4 r

Subtract the terms

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Evaluate

- r - 4 r

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

(- 1 - 4) r

Subtract the numbers

- 5 r

- 5 r - 37 + 12

Add the numbers

- 5 r - 25

- 5 r - 25 = 0

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

- 5 r = 0 + 25

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

- 5 r = 25

Change the signs on both sides of the equation

5 r = - 25

Divide both sides

\frac{5 r}{5} = \frac{- 25}{5}

Divide the numbers

r = \frac{- 25}{5}

Solution

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Evaluate

\frac{- 25}{5}

Reduce the numbers

\frac{- 5}{1}

Calculate

- 5

r = - 5

Show Solution

Rewrite the equation

x^{2} + y^{2} = 25

Evaluate

6 r - 37 = 7 r - 4 (3 - r)

Evaluate

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Evaluate

7 r - 4 (3 - r)

Expand the expression

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Calculate

- 4 (3 - r)

Apply the distributive property

- 4 \times 3 - (- 4 r)

Multiply the numbers

- 12 - (- 4 r)

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 r

7 r - 12 + 4 r

Add the terms

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Evaluate

7 r + 4 r

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

(7 + 4) r

Add the numbers

11 r

11 r - 12

6 r - 37 = 11 r - 12

Rewrite the expression

- 5 r = 37 - 12

Simplify the expression

- 5 r = 25

Square both sides of the equation

(- 5 r)^{2} = 2 5^{2}

Evaluate

25 r^{2} = 2 5^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

25 (x^{2} + y^{2}) = 2 5^{2}

Evaluate the power

25 (x^{2} + y^{2}) = 625

Solution

x^{2} + y^{2} = 25

Show Solution

Solve the equation

Rewrite the equation

Graph