Solve the following compound inequality.
5x + 7 ≤ -3 OR 3x - 4 ≥ 11

A. -2 ≤ x ≤ 5

B. x ≤ -2 OR x ≥ 5

C. x ≤ -15 OR x ≥ 12

D. x ≥ 5

Thank you!

Answers

Answer 1

Answer:

B

Step-by-step explanation:

We have the compound inequality:

[tex]5x+7\leq-3 \text{ or } 3x-4\geq 11[/tex]

Since this is an “OR” inequality, we can solve each inequality individually. So:

1)

We have:

[tex]5x+7\leq-3[/tex]

Subtract 7 from both sides:

[tex]5x\leq -10[/tex]

Divide both sides by 5:

[tex]x\leq-2[/tex]

So, the first solution is above.

2)

We have:

[tex]3x-4\geq 11[/tex]

Add 4 to both sides:

[tex]3x\geq15[/tex]

Divide both side by 3:

[tex]x\geq5[/tex]

Our second solution is above.

Therefore, our solution is:

[tex]x\leq -2 \text{ or } x\geq5[/tex]

Since our original inequality is “OR,” our solution set remains an “OR.”

Hence, our answer is B.


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Answer:

Option 1:[tex]y = -\frac{2}{3}x+5[/tex] is the correct answer.

Step-by-step explanation:

The slope-intercept form of a line is given as:

[tex]y = mx+b[/tex]

Here m is the slope and b is the y-intercept

m is calculated using the formula

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

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[tex](x_1,y_1) = (-3,7)\\(x_2,y_2) = (9,-1)[/tex]

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[tex]m = \frac{-1-7}{9+3}\\= \frac{-8}{12}\\=\frac{-2}{3}[/tex]

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[tex]y= -\frac{2}{3}x+b[/tex]

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Putting the value of b

[tex]y = -\frac{2}{3}x+5[/tex]

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Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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Answers

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Answers

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Answer:

Step-by-step explanation:

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