Solve 2(x-2)-3(4x-1)=9(x-1)

Question

Solve the equation

x = \frac{8}{19}

Alternative Form

x \approx 0.421053

Evaluate

2 (x - 2) - 3 (4 x - 1) = 9 (x - 1)

Calculate

More Steps

Evaluate

2 (x - 2) - 3 (4 x - 1)

Expand the expression

More Steps

Calculate

2 (x - 2)

Apply the distributive property

2 x - 2 \times 2

Multiply the numbers

2 x - 4

2 x - 4 - 3 (4 x - 1)

Expand the expression

More Steps

Calculate

- 3 (4 x - 1)

Apply the distributive property

- 3 \times 4 x - (- 3 \times 1)

Multiply the numbers

- 12 x - (- 3 \times 1)

Any expression multiplied by 1 remains the same

- 12 x - (- 3)

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 x + 3

2 x - 4 - 12 x + 3

Subtract the terms

More Steps

Evaluate

2 x - 12 x

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

(2 - 12) x

Subtract the numbers

- 10 x

- 10 x - 4 + 3

Add the numbers

- 10 x - 1

- 10 x - 1 = 9 (x - 1)

Calculate

More Steps

Evaluate

9 (x - 1)

Apply the distributive property

9 x - 9 \times 1

Any expression multiplied by 1 remains the same

9 x - 9

- 10 x - 1 = 9 x - 9

Move the expression to the left side

- 10 x - 1 - (9 x - 9) = 0

Calculate

More Steps

Add the terms

- 10 x - 1 - (9 x - 9)

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

- 10 x - 1 - 9 x + 9

Subtract the terms

More Steps

Evaluate

- 10 x - 9 x

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

(- 10 - 9) x

Subtract the numbers

- 19 x

- 19 x - 1 + 9

Add the numbers

- 19 x + 8

- 19 x + 8 = 0

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

- 19 x = 0 - 8

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

- 19 x = - 8

Change the signs on both sides of the equation

19 x = 8

Divide both sides

\frac{19 x}{19} = \frac{8}{19}

Solution

x = \frac{8}{19}

Alternative Form

x \approx 0.421053

Show Solution

Rewrite the equation

19 x = 8

Evaluate

2 (x - 2) - 3 (4 x - 1) = 9 (x - 1)

Evaluate

More Steps

Evaluate

2 (x - 2) - 3 (4 x - 1)

Expand the expression

More Steps

Calculate

2 (x - 2)

Apply the distributive property

2 x - 2 \times 2

Multiply the numbers

2 x - 4

2 x - 4 - 3 (4 x - 1)

Expand the expression

More Steps

Calculate

- 3 (4 x - 1)

Apply the distributive property

- 3 \times 4 x - (- 3 \times 1)

Multiply the numbers

- 12 x - (- 3 \times 1)

Any expression multiplied by 1 remains the same

- 12 x - (- 3)

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 x + 3

2 x - 4 - 12 x + 3

Subtract the terms

More Steps

Evaluate

2 x - 12 x

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

(2 - 12) x

Subtract the numbers

- 10 x

- 10 x - 4 + 3

Add the numbers

- 10 x - 1

- 10 x - 1 = 9 (x - 1)

Multiply

More Steps

Evaluate

9 (x - 1)

Apply the distributive property

9 x - 9 \times 1

Any expression multiplied by 1 remains the same

9 x - 9

- 10 x - 1 = 9 x - 9

Move the variable to the left side

- 19 x - 1 = - 9

Move the constant to the right side

- 19 x = - 8

Solution

19 x = 8

Show Solution

Solve the equation

Rewrite the equation

Graph