Solve (6a-22sqrt(106a))/18<0

Question

Solve the inequality

0 < a < \frac{12826}{9}

Alternative Form

a \in (0, \frac{12826}{9})

Evaluate

\frac{6 a - 22 106 a}{18} < 0

Find the domain

More Steps

\frac{6 a - 22 106 a}{18} < 0, a \geq 0

Divide the terms

More Steps

\frac{3 a - 11 106 a}{9} < 0

Multiply both sides of the inequality by 9

\frac{3 a - 11 106 a}{9} \times 9 < 0 \times 9

Multiply the terms

3 a - 11 106 a < 0 \times 9

Multiply the terms

3 a - 11 106 a < 0

Move the expression to the right side

- 11 106 a < - 3 a

Change the signs on both sides of the inequality and flip the inequality sign

11 106 a > 3 a

Separate the inequality into 2 possible cases

11 106 a > 3 a, 3 a \geq 0 11 106 a > 3 a, 3 a < 0

Solve the inequality

More Steps

0 < a < \frac{12826}{9}, 3 a \geq 0 11 106 a > 3 a, 3 a < 0

Solve the inequality

0 < a < \frac{12826}{9}, a \geq 0 11 106 a > 3 a, 3 a < 0

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of a

0 < a < \frac{12826}{9}, a \geq 0 a \in R, 3 a < 0

Solve the inequality

0 < a < \frac{12826}{9}, a \geq 0 a \in R, a < 0

Find the intersection

0 < a < \frac{12826}{9} a \in R, a < 0

Find the intersection

0 < a < \frac{12826}{9} a < 0

Find the union

a \in (- \infty, 0) \cup (0, \frac{12826}{9})

Check if the solution is in the defined range

a \in (- \infty, 0) \cup (0, \frac{12826}{9}), a \geq 0

Solution

0 < a < \frac{12826}{9}

Alternative Form

a \in (0, \frac{12826}{9})

Show Solution