Solve 6-8(x-1)=8-2(x-7)

Question

Solve the equation

x = - \frac{4}{3}

Alternative Form

x = - 1. \dot{3}

Evaluate

6 - 8 (x - 1) = 8 - 2 (x - 7)

Move the expression to the left side

6 - 8 (x - 1) - (8 - 2 (x - 7)) = 0

Subtract the terms

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Evaluate

6 - 8 (x - 1) - (8 - 2 (x - 7))

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 - 8 (x - 1) - 8 + 2 (x - 7)

Subtract the numbers

- 2 - 8 (x - 1) + 2 (x - 7)

- 2 - 8 (x - 1) + 2 (x - 7) = 0

Calculate the sum or difference

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Evaluate

- 2 - 8 (x - 1) + 2 (x - 7)

Expand the expression

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Calculate

- 8 (x - 1)

Apply the distributive property

- 8 x - (- 8 \times 1)

Any expression multiplied by 1 remains the same

- 8 x - (- 8)

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

- 8 x + 8

- 2 - 8 x + 8 + 2 (x - 7)

Expand the expression

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Calculate

2 (x - 7)

Apply the distributive property

2 x - 2 \times 7

Multiply the numbers

2 x - 14

- 2 - 8 x + 8 + 2 x - 14

Calculate the sum or difference

- 8 - 8 x + 2 x

Add the terms

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Evaluate

- 8 x + 2 x

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

(- 8 + 2) x

Add the numbers

- 6 x

- 8 - 6 x

- 8 - 6 x = 0

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

- 6 x = 0 + 8

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

- 6 x = 8

Change the signs on both sides of the equation

6 x = - 8

Divide both sides

\frac{6 x}{6} = \frac{- 8}{6}

Divide the numbers

x = \frac{- 8}{6}

Solution

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Evaluate

\frac{- 8}{6}

Cancel out the common factor 2

\frac{- 4}{3}

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

- \frac{4}{3}

x = - \frac{4}{3}

Alternative Form

x = - 1. \dot{3}

Show Solution

Rewrite the equation

3 x = - 4

Evaluate

6 - 8 (x - 1) = 8 - 2 (x - 7)

Evaluate

More Steps

Evaluate

6 - 8 (x - 1)

Expand the expression

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Calculate

- 8 (x - 1)

Apply the distributive property

- 8 x - (- 8 \times 1)

Any expression multiplied by 1 remains the same

- 8 x - (- 8)

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

- 8 x + 8

6 - 8 x + 8

Add the numbers

14 - 8 x

14 - 8 x = 8 - 2 (x - 7)

Evaluate

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Evaluate

8 - 2 (x - 7)

Expand the expression

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Calculate

- 2 (x - 7)

Apply the distributive property

- 2 x - (- 2 \times 7)

Multiply the numbers

- 2 x - (- 14)

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

- 2 x + 14

8 - 2 x + 14

Add the numbers

22 - 2 x

14 - 8 x = 22 - 2 x

Move the variable to the left side

14 - 6 x = 22

Move the constant to the right side

- 6 x = 8

Multiply both sides

6 x = - 8

Solution

3 x = - 4

Show Solution

Solve the equation

Rewrite the equation

Graph