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Yuki888 [10]
3 years ago
12

1. Solve the compound inequality. You do not need to graph the solution.

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
7 0

Answer:

9 ≤ x ≤ 7

Step-by-step explanation:

2x – 3 ≤ 11 or –8x – 10 ≤ – 82

We shall determine the value of x in both case.

2x – 3 ≤ 11

Collect like terms

2x ≤ 11 + 3

2x ≤ 14

Divide both side by 2

x ≤ 14/2

x ≤ 7

–8x – 10 ≤ – 82

Collect like terms

–8x ≤ – 82 + 10

–8x ≤ – 72

Divide both side by –8

x ≤ – 72 / –8

x ≥ 9 (since we divided by a negative sign)

9 ≤ x

Combining both answers

x ≤ 7

9 ≤ x

Thus,

9 ≤ x ≤ 7

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Hey there! How are you today?

First, when dealing with the Distributive Property, we always need to pay attention to what number/variable we are multiplying by.
The concept of the Distributive Property is to look at the number/variable outside of the parenthesis and then multiply it by all numbers/variables inside of the parenthesis individually, and then sum those products up.

If you're having trouble grasping this concept, here's an example:

Ex:
2(1 + 3)
Multiply the number outside of the parenthesis (2) by all numbers inside of the parenthesis (1 and 3) individually.
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Simplify the multiplication process.
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Sum up our products.
8.
8 is our answer for this example.

Now that we've explained and practiced what we are working on, let's apply this concept to the real problem.

7(2x^2 + 9x - 3)
Multiply the number outside of the parenthesis (7) by all numbers/variables inside of the parenthesis (2x^2, 9x, and -3).
7(2x^2) + 7(9x) + 7(-3)
Simplify the first multiplication parenthesis.
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Simplify the second multiplication parenthesis.
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Simplify the third and final multiplication parenthesis.
7*(-3) = -21 (When you multiply a positive by a negative, your product is negative).

Now, let's write down our final products as a whole answer. Remember to start from the highest exponent.

14x^2 + 21x - 21 is your final expression.

I hope this helps! Let me know if you have any questions or concerns down in the comment box below this answer, and I'll get back to you when I can.
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