Solve root(2)(5-x)<x 7

Question

Solve the inequality

\frac{3 109 - 1}{98} < x \leq 5

Alternative Form

x \in (\frac{3 109 - 1}{98}, 5]

Evaluate

5 - x < x \times 7

Find the domain

More Steps

5 - x < x \times 7, x \leq 5

Use the commutative property to reorder the terms

5 - x < 7 x

Separate the inequality into 2 possible cases

5 - x < 7 x, 7 x \geq 0 5 - x < 7 x, 7 x < 0

Solve the inequality

More Steps

x \in (- \infty, - \frac{3 109 + 1}{98}) \cup (\frac{3 109 - 1}{98}, + \infty), 7 x \geq 0 5 - x < 7 x, 7 x < 0

Solve the inequality

x \in (- \infty, - \frac{3 109 + 1}{98}) \cup (\frac{3 109 - 1}{98}, + \infty), x \geq 0 5 - x < 7 x, 7 x < 0

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

x \in (- \infty, - \frac{3 109 + 1}{98}) \cup (\frac{3 109 - 1}{98}, + \infty), x \geq 0 x \in \emptyset, 7 x < 0

Solve the inequality

x \in (- \infty, - \frac{3 109 + 1}{98}) \cup (\frac{3 109 - 1}{98}, + \infty), x \geq 0 x \in \emptyset, x < 0

Find the intersection

x > \frac{3 109 - 1}{98} x \in \emptyset, x < 0

Find the intersection

x > \frac{3 109 - 1}{98} x \in \emptyset

Find the union

x > \frac{3 109 - 1}{98}

Check if the solution is in the defined range

x > \frac{3 109 - 1}{98}, x \leq 5

Solution

\frac{3 109 - 1}{98} < x \leq 5

Alternative Form

x \in (\frac{3 109 - 1}{98}, 5]

Show Solution