Solve |8 y| = 2y - 3

Question

Solve the equation

y \in \emptyset

Alternative Form

No solution

Evaluate

∣ 8 y ∣ = 2 y - 3

Rewrite the expression

∣ 8 y ∣ - 2 y + 3 = 0

Separate the equation into 2 possible cases

8 y - 2 y + 3 = 0, 8 y \geq 0 - 8 y - 2 y + 3 = 0, 8 y < 0

Solve the equation

More Steps

Evaluate

8 y - 2 y + 3 = 0

Calculate

More Steps

Evaluate

8 y - 2 y

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

(8 - 2) y

Subtract the numbers

6 y

6 y + 3 = 0

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

6 y = 0 - 3

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

6 y = - 3

Divide both sides

\frac{6 y}{6} = \frac{- 3}{6}

Divide the numbers

y = \frac{- 3}{6}

Divide the numbers

More Steps

Evaluate

\frac{- 3}{6}

Cancel out the common factor 3

\frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{2}

y = - \frac{1}{2}

y = - \frac{1}{2}, 8 y \geq 0 - 8 y - 2 y + 3 = 0, 8 y < 0

Solve the inequality

y = - \frac{1}{2}, y \geq 0 - 8 y - 2 y + 3 = 0, 8 y < 0

Solve the equation

More Steps

Evaluate

- 8 y - 2 y + 3 = 0

Calculate

More Steps

Evaluate

- 8 y - 2 y

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

(- 8 - 2) y

Subtract the numbers

- 10 y

- 10 y + 3 = 0

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

- 10 y = 0 - 3

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

- 10 y = - 3

Change the signs on both sides of the equation

10 y = 3

Divide both sides

\frac{10 y}{10} = \frac{3}{10}

Divide the numbers

y = \frac{3}{10}

y = - \frac{1}{2}, y \geq 0 y = \frac{3}{10}, 8 y < 0

Solve the inequality

y = - \frac{1}{2}, y \geq 0 y = \frac{3}{10}, y < 0

Find the intersection

y \in \emptyset y = \frac{3}{10}, y < 0

Find the intersection

y \in \emptyset y \in \emptyset

Solution

y \in \emptyset

Alternative Form

No solution

Show Solution