Solve |x-1| |2x-1|

Question

Simplify the expression

2 x^{2} - 3 x + 1

Evaluate

∣ x - 1 ∣ ∣ 2 x - 1 ∣

Multiply the terms

∣ (x - 1) (2 x - 1) ∣

Solution

More Steps

Evaluate

(x - 1) (2 x - 1)

Apply the distributive property

x \times 2 x - x \times 1 - 2 x - (- 1)

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 1 - 2 x - (- 1)

Any expression multiplied by 1 remains the same

2 x^{2} - x - 2 x - (- 1)

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^{2} - x - 2 x + 1

Subtract the terms

More Steps

Evaluate

- x - 2 x

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

(- 1 - 2) x

Subtract the numbers

- 3 x

2 x^{2} - 3 x + 1

2 x^{2} - 3 x + 1

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Evaluate

∣ x - 1 ∣ ∣ 2 x - 1 ∣

To find the roots of the expression,set the expression equal to 0

∣ x - 1 ∣ ∣ 2 x - 1 ∣ = 0

Multiply the terms

∣ (x - 1) (2 x - 1) ∣ = 0

Rewrite the expression

(x - 1) (2 x - 1) = 0

Separate the equation into 2 possible cases

x - 1 = 0 2 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 2 x - 1 = 0

Solve the equation

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 1 x = \frac{1}{2}

Solution

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Show Solution