What is 5/3 x+(2x+1)(1/3 x-1)>= 0 ?

The solution to 5/3 x+(2x+1)(1/3 x-1)>= 0 is x = sqrt(3/2)

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5/3 x+(2x+1)(1/3 x-1)>= 0

\frac{5}{3} x + (2 x + 1) (\frac{1}{3} x - 1) \geq 0

x \leq - \frac{3}{2} or x \geq \frac{3}{2}

Interval Notation

(- \infty, - \frac{3}{2}] \cup [\frac{3}{2}, \infty)

Decimal Notation

x \leq - 1.22474 \dots or x \geq 1.22474 \dots

Solution steps

\frac{5}{3} x + (2 x + 1) (\frac{1}{3} x - 1) \geq 0

Expand

\frac{5}{3} x + (2 x + 1) (\frac{1}{3} x - 1) : \frac{2 x ^{2}}{3} - 1

\frac{2 x ^{2}}{3} - 1 \geq 0

Move

1

to the right side

\frac{2 x ^{2}}{3} \geq 1

Multiply both sides by

3

2 x^{2} \geq 3

Divide both sides by

2

x^{2} \geq \frac{3}{2}

For

u^{n} \geq a

, if

n

is even then

x \leq - \frac{3}{2} or x \geq \frac{3}{2}

10 + j 5

9.8 \cdot 2

7 x^{2} + 8 x - 4 = 0

x^{2} - 19 x + 48

0.3 x + 1.38 = 0.24 x + 1.2

What is 5/3 x+(2x+1)(1/3 x-1)>= 0 ?
The solution to 5/3 x+(2x+1)(1/3 x-1)>= 0 is x<=-sqrt(3/2)\lor x>= sqrt(3/2)