Solve 2x-7=|x| 1 - ScanMath

Question

Solve the equation

x = 7

Evaluate

2 x - 7 = ∣ x ∣ \times 1

Any expression multiplied by 1 remains the same

2 x - 7 = ∣ x ∣

Swap the sides

∣ x ∣ = 2 x - 7

Rewrite the expression

∣ x ∣ - 2 x + 7 = 0

Separate the equation into 2 possible cases

x - 2 x + 7 = 0, x \geq 0 - x - 2 x + 7 = 0, x < 0

Solve the equation

More Steps

Evaluate

x - 2 x + 7 = 0

Calculate

More Steps

Evaluate

x - 2 x

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

(1 - 2) x

Subtract the numbers

- x

- x + 7 = 0

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

- x = 0 - 7

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

- x = - 7

Change the signs on both sides of the equation

x = 7

x = 7, x \geq 0 - x - 2 x + 7 = 0, x < 0

Solve the equation

More Steps

Evaluate

- x - 2 x + 7 = 0

Calculate

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

- 3 x + 7 = 0

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

- 3 x = 0 - 7

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

- 3 x = - 7

Change the signs on both sides of the equation

3 x = 7

Divide both sides

\frac{3 x}{3} = \frac{7}{3}

Divide the numbers

x = \frac{7}{3}

x = 7, x \geq 0 x = \frac{7}{3}, x < 0

Find the intersection

x = 7 x = \frac{7}{3}, x < 0

Find the intersection

x = 7 x \in \emptyset

Solution

x = 7

Show Solution