Solve 52x = 3(2x - 5) - 8

Question

Solve the equation

x = - \frac{1}{2}

Alternative Form

x = - 0.5

Evaluate

52 x = 3 (2 x - 5) - 8

Move the expression to the left side

52 x - (3 (2 x - 5) - 8) = 0

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

52 x - 3 (2 x - 5) + 8 = 0

Calculate the sum or difference

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Evaluate

52 x - 3 (2 x - 5) + 8

Expand the expression

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Calculate

- 3 (2 x - 5)

Apply the distributive property

- 3 \times 2 x - (- 3 \times 5)

Multiply the numbers

- 6 x - (- 3 \times 5)

Multiply the numbers

- 6 x - (- 15)

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 x + 15

52 x - 6 x + 15 + 8

Subtract the terms

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Evaluate

52 x - 6 x

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

(52 - 6) x

Subtract the numbers

46 x

46 x + 15 + 8

Add the numbers

46 x + 23

46 x + 23 = 0

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

46 x = 0 - 23

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

46 x = - 23

Divide both sides

\frac{46 x}{46} = \frac{- 23}{46}

Divide the numbers

x = \frac{- 23}{46}

Solution

More Steps

Evaluate

\frac{- 23}{46}

Cancel out the common factor 23

\frac{- 1}{2}

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

- \frac{1}{2}

x = - \frac{1}{2}

Alternative Form

x = - 0.5

Show Solution

Rewrite the equation

2 x = - 1

Evaluate

52 x = 3 (2 x - 5) - 8

Evaluate

More Steps

Evaluate

3 (2 x - 5) - 8

Expand the expression

More Steps

Calculate

3 (2 x - 5)

Apply the distributive property

3 \times 2 x - 3 \times 5

Multiply the numbers

6 x - 3 \times 5

Multiply the numbers

6 x - 15

6 x - 15 - 8

Subtract the numbers

6 x - 23

52 x = 6 x - 23

Move the variable to the left side

46 x = - 23

Solution

2 x = - 1

Show Solution

Solve the equation

Rewrite the equation

Graph