What is ((3x-4))/2 <((4x-5))/3 ?

The solution to ((3x-4))/2 <((4x-5))/3 is x<2

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((3x-4))/2 <((4x-5))/3

\frac{( 3 x - 4 )}{2} < \frac{( 4 x - 5 )}{3}

x < 2

Interval Notation

(- \infty, 2)

Solution steps

\frac{( 3 x - 4 )}{2} < \frac{( 4 x - 5 )}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(3 x - 4) \cdot 3 < 2 (4 x - 5)

Expand

(3 x - 4) \cdot 3 : 9 x - 12

Expand

2 (4 x - 5) : 8 x - 10

9 x - 12 < 8 x - 10

Move

12

to the right side

9 x < 8 x + 2

Move

8 x

to the left side

x < 2

5 - 3 x > 7

x + \frac{3}{8} - \frac{21}{3} > \frac{5}{4}

x + 2 x > 6

42 x + 1 > 0.16

x - 4 \geq 12