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

The solution to (2x+5)/3 >= (3x-1)/2 is x<= 13/5

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

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

x \leq \frac{13}{5}

Interval Notation

(- \infty, \frac{13}{5}]

Decimal Notation

x \leq 2.6

Solution steps

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

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(2 x + 5) \cdot 2 \geq 3 (3 x - 1)

Expand

(2 x + 5) \cdot 2 : 4 x + 10

Expand

3 (3 x - 1) : 9 x - 3

4 x + 10 \geq 9 x - 3

Move

10

to the right side

4 x \geq 9 x - 13

Move

9 x

to the left side

- 5 x \geq - 13

Multiply both sides by

- 1

5 x \leq 13

Divide both sides by

5

x \leq \frac{13}{5}

(- \frac{x}{4 - x ^{2}})^{2}

3 \cdot 3

4 x - 9 = 15

2 x + 6 \leq - 2

x^{2} - 12 x - 13 = 0