Solve 1 - |3x| = 9x

Question

Solve the equation

x = \frac{1}{12}

Alternative Form

x = 0.08 \dot{3}

Evaluate

1 - ∣ 3 x ∣ = 9 x

Move the expression to the left side

1 - ∣ 3 x ∣ - 9 x = 0

Separate the equation into 2 possible cases

1 - 3 x - 9 x = 0, 3 x \geq 0 1 - (- 3 x) - 9 x = 0, 3 x < 0

Solve the equation

More Steps

Evaluate

1 - 3 x - 9 x = 0

Calculate

More Steps

Evaluate

- 3 x - 9 x

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

(- 3 - 9) x

Subtract the numbers

- 12 x

1 - 12 x = 0

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

- 12 x = 0 - 1

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

- 12 x = - 1

Change the signs on both sides of the equation

12 x = 1

Divide both sides

\frac{12 x}{12} = \frac{1}{12}

Divide the numbers

x = \frac{1}{12}

x = \frac{1}{12}, 3 x \geq 0 1 - (- 3 x) - 9 x = 0, 3 x < 0

Solve the inequality

x = \frac{1}{12}, x \geq 0 1 - (- 3 x) - 9 x = 0, 3 x < 0

Solve the equation

More Steps

Evaluate

1 - (- 3 x) - 9 x = 0

Calculate

1 + 3 x - 9 x = 0

Calculate

More Steps

Evaluate

3 x - 9 x

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

(3 - 9) x

Subtract the numbers

- 6 x

1 - 6 x = 0

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

- 6 x = 0 - 1

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

- 6 x = - 1

Change the signs on both sides of the equation

6 x = 1

Divide both sides

\frac{6 x}{6} = \frac{1}{6}

Divide the numbers

x = \frac{1}{6}

x = \frac{1}{12}, x \geq 0 x = \frac{1}{6}, 3 x < 0

Solve the inequality

x = \frac{1}{12}, x \geq 0 x = \frac{1}{6}, x < 0

Find the intersection

x = \frac{1}{12} x = \frac{1}{6}, x < 0

Find the intersection

x = \frac{1}{12} x \in \emptyset

Solution

x = \frac{1}{12}

Alternative Form

x = 0.08 \dot{3}

Show Solution