Solve 1-|3x|=6x - ScanMath

Question

Solve the equation

x = \frac{1}{9}

Alternative Form

x = 0. \dot{1}

Evaluate

1 - ∣ 3 x ∣ = 6 x

Move the expression to the left side

1 - ∣ 3 x ∣ - 6 x = 0

Separate the equation into 2 possible cases

1 - 3 x - 6 x = 0, 3 x \geq 0 1 - (- 3 x) - 6 x = 0, 3 x < 0

Solve the equation

More Steps

Evaluate

1 - 3 x - 6 x = 0

Calculate

More Steps

Evaluate

- 3 x - 6 x

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

(- 3 - 6) x

Subtract the numbers

- 9 x

1 - 9 x = 0

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

- 9 x = 0 - 1

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

- 9 x = - 1

Change the signs on both sides of the equation

9 x = 1

Divide both sides

\frac{9 x}{9} = \frac{1}{9}

Divide the numbers

x = \frac{1}{9}

x = \frac{1}{9}, 3 x \geq 0 1 - (- 3 x) - 6 x = 0, 3 x < 0

Solve the inequality

x = \frac{1}{9}, x \geq 0 1 - (- 3 x) - 6 x = 0, 3 x < 0

Solve the equation

More Steps

Evaluate

1 - (- 3 x) - 6 x = 0

Calculate

1 + 3 x - 6 x = 0

Calculate

More Steps

Evaluate

3 x - 6 x

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

(3 - 6) x

Subtract the numbers

- 3 x

1 - 3 x = 0

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

- 3 x = 0 - 1

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

- 3 x = - 1

Change the signs on both sides of the equation

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{9}, x \geq 0 x = \frac{1}{3}, 3 x < 0

Solve the inequality

x = \frac{1}{9}, x \geq 0 x = \frac{1}{3}, x < 0

Find the intersection

x = \frac{1}{9} x = \frac{1}{3}, x < 0

Find the intersection

x = \frac{1}{9} x \in \emptyset

Solution

x = \frac{1}{9}

Alternative Form

x = 0. \dot{1}

Show Solution