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Thepotemich [5.8K]
2 years ago
8

|3y-1|>5 Solve the absolute value inequalities by making a compound inequality

Mathematics
1 answer:
Fantom [35]2 years ago
7 0

Hi there!

We can begin by solving the inequality using the positive and negative terms:

3y - 1 > 5

Add 1 to both sides:

3y > 6

Divide both sides by 3:

y > 2

Now, solve the negative:

-(3y - 1) > 5

Distribute the -1:

-3y + 1 > 5

Subtract 1 from both sides:

-3y > 4

Divide both sides by -3. REMEMBER to flip the sign.

y < -4/3

'y' has to be LESS than -4/3 and greater than 2, so:

y < -4/3, y > 2

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Arisa [49]

ANSWER

D. 13

EXPLANATION

We have

f(x) =  \frac{2x + 1}{x - 4}

To find

{f}^{ - 1} (3)

means we want to find an x-value whose image is 3.

\frac{2x + 1}{x - 4}  = 3

We cross multiply,

2x + 1 = 3(x - 4)

Expand:

2x + 1 = 3x - 12

Combine like terms,

3x - 2x = 12 + 1

x = 13

\therefore{f}^{ - 1} (3)= 13

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Answer: function 1

Rate of change of function 1:
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To find the gradient (rate of change):
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