Solve 8-2|4-5y|=4

Question

Solve the equation

y_{1} = \frac{2}{5}, y_{2} = \frac{6}{5}

Alternative Form

y_{1} = 0.4, y_{2} = 1.2

Evaluate

8 - 2 ∣ 4 - 5 y ∣ = 4

Move the expression to the left side

8 - 2 ∣ 4 - 5 y ∣ - 4 = 0

Subtract the numbers

4 - 2 ∣ 4 - 5 y ∣ = 0

Separate the equation into 2 possible cases

4 - 2 (4 - 5 y) = 0, 4 - 5 y \geq 0 4 - 2 (- (4 - 5 y)) = 0, 4 - 5 y < 0

Solve the equation

More Steps

y = \frac{2}{5}, 4 - 5 y \geq 0 4 - 2 (- (4 - 5 y)) = 0, 4 - 5 y < 0

Solve the inequality

More Steps

y = \frac{2}{5}, y \leq \frac{4}{5} 4 - 2 (- (4 - 5 y)) = 0, 4 - 5 y < 0

Solve the equation

More Steps

y = \frac{2}{5}, y \leq \frac{4}{5} y = \frac{6}{5}, 4 - 5 y < 0

Solve the inequality

More Steps

y = \frac{2}{5}, y \leq \frac{4}{5} y = \frac{6}{5}, y > \frac{4}{5}

Find the intersection

y = \frac{2}{5} y = \frac{6}{5}, y > \frac{4}{5}

Find the intersection

y = \frac{2}{5} y = \frac{6}{5}

Solution

y_{1} = \frac{2}{5}, y_{2} = \frac{6}{5}

Alternative Form

y_{1} = 0.4, y_{2} = 1.2

Show Solution