What is ((b)(2(x-1)))/5 <= ((3(2+x)))/7 ?

The solution to ((b)(2(x-1)))/5 15/14

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((b)(2(x-1)))/5 <= ((3(2+x)))/7

\frac{( b ) ( 2 ( x - 1 ) )}{5} \leq \frac{( 3 ( 2 + x ) )}{7}

x \leq \frac{30 + 14 b}{14 b - 15}; b > \frac{15}{14}

Solution steps

\frac{( b ) ( 2 ( x - 1 ) )}{5} \leq \frac{( 3 ( 2 + x ) )}{7}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

b \cdot 2 (x - 1) \cdot 7 \leq 5 \cdot 3 (2 + x)

Simplify

14 b (x - 1) \leq 15 (2 + x)

Expand

14 b (x - 1) : 14 b x - 14 b

Expand

15 (2 + x) : 30 + 15 x

14 b x - 14 b \leq 30 + 15 x

Move

14 b

to the right side

14 b x \leq 30 + 15 x + 14 b

Move

15 x

to the left side

14 b x - 15 x \leq 30 + 14 b

Factor

14 b x - 15 x : x (14 b - 15)

x (14 b - 15) \leq 30 + 14 b

Divide both sides by

14 b - 15; b > \frac{15}{14}

x \leq \frac{30 + 14 b}{14 b - 15}; b > \frac{15}{14}

23 x - 27 - 13 x < 129 - 6

3 (x - 5) + 4 \leq 4 x - 18

\frac{5 x + 1}{6} > \frac{2 - 2 x + 1}{3}

x > 57 + x

a, a - b < 0

What is ((b)(2(x-1)))/5 <= ((3(2+x)))/7 ?
The solution to ((b)(2(x-1)))/5 <= ((3(2+x)))/7 is x<= (30+14b)/(14b-15);\quad b> 15/14