Solve 1- x/2 ≤ 2/3 (x(1-x))/6

Question

1 - \frac{x}{2} \leq \frac{2}{3} \times \frac{x ( 1 - x )}{6}

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in \emptyset

Alternative Form

No solution

Evaluate

1 - \frac{x}{2} \leq \frac{2}{3} \times \frac{x ( 1 - x )}{6}

Multiply the terms

More Steps

1 - \frac{x}{2} \leq \frac{x ( 1 - x )}{9}

Multiply both sides of the inequality by 18

(1 - \frac{x}{2}) \times 18 \leq \frac{x ( 1 - x )}{9} \times 18

Multiply the terms

More Steps

18 - 9 x \leq \frac{x ( 1 - x )}{9} \times 18

Multiply the terms

More Steps

18 - 9 x \leq 2 x - 2 x^{2}

Move the expression to the left side

18 - 9 x - (2 x - 2 x^{2}) \leq 0

Subtract the terms

More Steps

18 - 11 x + 2 x^{2} \leq 0

Rewrite the expression

18 - 11 x + 2 x^{2} = 0

Add or subtract both sides

- 11 x + 2 x^{2} = - 18

Divide both sides

\frac{- 11 x + 2 x ^{2}}{2} = \frac{- 18}{2}

Evaluate

- \frac{11}{2} x + x^{2} = - 9

Add the same value to both sides

- \frac{11}{2} x + x^{2} + \frac{121}{16} = - 9 + \frac{121}{16}

Simplify the expression

(x - \frac{11}{4})^{2} = - \frac{23}{16}

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 / R

There are no key numbers,so choose any value to test,for example x = 0

x = 0

Solution

More Steps

x \in \emptyset

Alternative Form

No solution

Show Solution