Solve |x-1| 2|x-4|=8

Question

Solve the equation

x_{1} = 0, x_{2} = 5

Evaluate

∣ x - 1 ∣ \times 2 ∣ x - 4 ∣ = 8

Multiply the terms

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Evaluate

∣ x - 1 ∣ \times 2 ∣ x - 4 ∣

Multiply the first two terms

2 ∣ x - 1 ∣ ∣ x - 4 ∣

Multiply the terms

2 ∣ (x - 1) (x - 4) ∣

2 ∣ (x - 1) (x - 4) ∣ = 8

Divide both sides

\frac{2 ∣ ( x - 1 ) ( x - 4 ) ∣}{2} = \frac{8}{2}

Divide the numbers

∣ (x - 1) (x - 4) ∣ = \frac{8}{2}

Divide the numbers

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Evaluate

\frac{8}{2}

Reduce the numbers

\frac{4}{1}

Calculate

4

∣ (x - 1) (x - 4) ∣ = 4

Separate the equation into 2 possible cases

(x - 1) (x - 4) = 4 (x - 1) (x - 4) = - 4

Solve the equation for x

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Evaluate

(x - 1) (x - 4) = 4

Expand the expression

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Evaluate

(x - 1) (x - 4)

Apply the distributive property

x \times x - x \times 4 - x - (- 4)

Multiply the terms

x^{2} - x \times 4 - x - (- 4)

Use the commutative property to reorder the terms

x^{2} - 4 x - x - (- 4)

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

x^{2} - 4 x - x + 4

Subtract the terms

x^{2} - 5 x + 4

x^{2} - 5 x + 4 = 4

Cancel equal terms on both sides of the expression

x^{2} - 5 x = 0

Factor the expression

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Evaluate

x^{2} - 5 x

Rewrite the expression

x \times x - x \times 5

Factor out x from the expression

x (x - 5)

x (x - 5) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 5 = 0

Solve the equation for x

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Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 0 x = 5

x = 0 x = 5 (x - 1) (x - 4) = - 4

Solve the equation for x

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Evaluate

(x - 1) (x - 4) = - 4

Expand the expression

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Evaluate

(x - 1) (x - 4)

Apply the distributive property

x \times x - x \times 4 - x - (- 4)

Multiply the terms

x^{2} - x \times 4 - x - (- 4)

Use the commutative property to reorder the terms

x^{2} - 4 x - x - (- 4)

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

x^{2} - 4 x - x + 4

Subtract the terms

x^{2} - 5 x + 4

x^{2} - 5 x + 4 = - 4

Move the expression to the left side

x^{2} - 5 x + 4 - (- 4) = 0

Subtract the numbers

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Evaluate

4 - (- 4)

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

4 + 4

Add the numbers

8

x^{2} - 5 x + 8 = 0

Substitute a= 1,b= - 5 and c= 8 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 8}{2}

Simplify the expression

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Evaluate

(- 5)^{2} - 4 \times 8

Multiply the numbers

(- 5)^{2} - 32

Rewrite the expression

5^{2} - 32

Evaluate the power

25 - 32

Subtract the numbers

- 7

x = \frac{5 \pm - 7}{2}

The expression is undefined in the set of real numbers

x \in / R

x = 0 x = 5 x \in / R

Find the union

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Show Solution

Solve the equation

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