Solve the inequality Show your work-5/2(3x+4)<6-3x

Mathematics

1 answer:

Dafna11 [192]3 years ago

5 0

Answer:

The answer to your question is: x > - 32/9

Step-by-step explanation:

-5/2(3x+4)<6-3x

Multiply by 2 -5(3x + 4) < 12 - 6x

Simplify -15x - 20 < 12 - 6x

Add +6x -15x + 6x -20 < 12 - 6x + 6x

Simplify - 9x - 20 < 12

Add + 20 -9x -20 + 20 < 12 + 20

Simplify -9x < 32

Divide by -9 -9/-9 x > 32/-9

Simplify x > - 32/9

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Log (3x+1) - Log (2x+5)= 1

sleet_krkn [62]

Answer:

$\huge \red { \boxed{x = - \frac{49}{17}}}$

Step-by-step explanation:

$log(3x + 1) - log(2x + 5) = 1 \\ \\ log \: \frac{3x + 1}{2x + 5} = log \: 10..( \because \: log \: 10 = 1) \\ \\ \frac{3x + 1}{2x + 5} = 10 \\ \\ 3x + 1 = 20x + 50 \\ 3x - 20x = 50 - 1 \\ \\ - 17x = 49 \\ \\ x = \frac{49}{ - 17} \\ \\ \huge \purple{ \boxed{x = - \frac{49}{17}}} \\$