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Nookie1986 [14]
3 years ago
15

Solve the equation. Check your solutions. |4b+4|=|2b+8|

Mathematics
1 answer:
anzhelika [568]3 years ago
6 0

Answer:

<h2><u>b = 2 or b = -2</u></h2>

Explanation:

|4b + 4| = |2b + 8|

<em>Solve absolute value</em>

|4b + 4| = |2b + 8|

Either 4b + 4 = 2b + 8 or 4b + 4 = −(2b + 8)

4b + 4 = 2b + 8 <em>(Possibility 1)</em>

4b + 4 − 2b = 2b + 8 − 2b <em>(Subtract 2b from both sides)</em>

2b + 4 = 8

2b + 4 − 4 = 8 − 4 <em>(Subtract 4 from both sides)</em>

2b = 4

2b / 2 = 4 / 2 <em>(Divide both sides by 2)</em>

b = 2

4b + 4 = −(2b + 8) <em>(Possibility 2)</em>

4b + 4 = −2b − 8 <em>(Simplify both sides of the equation)</em>

4b + 4 + 2b = −2b − 8 + 2b <em>(Add 2b to both sides)</em>

6b + 4 = −8

6b + 4 − 4 = −8 − 4 <em>(Subtract 4 from both sides)</em>

6b = −12

6b / 6 = -12 / 6 <em>(Divide both sides by 6)</em>

b = -2

<h2><u>b = 2 or b = -2</u></h2>
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Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

<h3>How to find the production level that'll maximize profit?</h3>

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

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Also, revenue, R(x) = x × P(x)

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Next, we would differentiate the revenue function to derive the marginal revenue:

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Solving by using the quadratic equation, we have:

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Read more on maximized profit here: brainly.com/question/13800671

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