Solve (45 + x)/(105 + x) = 13/25

Question

Solve the equation

x = 20

Evaluate

\frac{45 + x}{105 + x} = \frac{13}{25}

Find the domain

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Evaluate

105 + x \neq = 0

Move the constant to the right side

x \neq = 0 - 105

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

x \neq = - 105

\frac{45 + x}{105 + x} = \frac{13}{25}, x \neq = - 105

Cross multiply

(45 + x) \times 25 = (105 + x) \times 13

Simplify the equation

25 (45 + x) = (105 + x) \times 13

Simplify the equation

25 (45 + x) = 13 (105 + x)

Calculate

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Evaluate

25 (45 + x)

Apply the distributive property

25 \times 45 + 25 x

Multiply the numbers

1125 + 25 x

1125 + 25 x = 13 (105 + x)

Calculate

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Evaluate

13 (105 + x)

Apply the distributive property

13 \times 105 + 13 x

Multiply the numbers

1365 + 13 x

1125 + 25 x = 1365 + 13 x

Move the expression to the left side

1125 + 25 x - (1365 + 13 x) = 0

Calculate the sum or difference

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Add the terms

1125 + 25 x - (1365 + 13 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

1125 + 25 x - 1365 - 13 x

Subtract the numbers

- 240 + 25 x - 13 x

Subtract the terms

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Evaluate

25 x - 13 x

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

(25 - 13) x

Subtract the numbers

12 x

- 240 + 12 x

- 240 + 12 x = 0

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

12 x = 0 + 240

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

12 x = 240

Divide both sides

\frac{12 x}{12} = \frac{240}{12}

Divide the numbers

x = \frac{240}{12}

Divide the numbers

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Evaluate

\frac{240}{12}

Reduce the numbers

\frac{20}{1}

Calculate

20

x = 20

Check if the solution is in the defined range

x = 20, x \neq = - 105

Solution

x = 20

Show Solution

Solve the equation

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