I need help math please what's the answer

Mathematics

2 answers:

Salsk061 [2.6K]4 years ago

8 0

Answer: Choice 3) 0, 3.9, and 5.1

Basically almost every value of that set but leaving out 10.2

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Explanation:

The given set of values is {0, 3.9, 5.1, 10.2}

Let's check each number of that set one value at a time.

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Checking x = 0

Replace every copy of x with 0, then use PEMDAS to simplify each side

We need to see if we get a true inequality or not

$8.9 - 0.3x \ge 0.8x$

$8.9 - 0.3*0 \ge 0.8*0$

$8.9 - 0 \ge 0$

$8.9 \ge 0$

The last inequality is TRUE (8.9 is greater than 0).

So x = 0 is part of the solution set.
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Checking x = 3.9

Repeat the same steps as done previously (with x = 0).

This time we replace every x with 3.9, but the remaining general steps are the same more or less.

$8.9 - 0.3x \ge 0.8x$

$8.9 - 0.3*3.9 \ge 0.8*3.9$

$8.9 - 1.17 \ge 3.12$

$7.73 \ge 3.12$

The last inequality is TRUE (7.73 is greater than 3.12).

The value x = 3.9 is also part of the solution set.
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Checking x = 5.1

Follow the same outline. This time we use 5.1 in place of x.

$8.9 - 0.3x \ge 0.8x$

$8.9 - 0.3*5.1 \ge 0.8*5.1$

$8.9 - 1.53 \ge 4.08$

$7.37 \ge 4.08$

The last inequality is TRUE (7.37 is greater than 4.08).

The value x = 5.1 joins in with the other two values that are part of the solution set.
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Checking x = 10.2

Now replace every x value with 10.2

$8.9 - 0.3x \ge 0.8x$

$8.9 - 0.3*10.2 \ge 0.8*10.2$

$8.9 - 3.06 \ge 8.16$

$5.84 \ge 8.16$

The last inequality is FALSE (5.84 is not larger than 8.16, nor is it it equal; 5.84 is smaller than 8.16).

Because we have a false inequality result, we can say that x = 10.2 is NOT part of the solution set.

If you want, you can use a red pen to cross off 10.2 to visually remind you that 10.2 is not part of the solution set.
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So in summary we found x = 0, x = 3.9 and x = 5.1 to satisfy (make true) the original inequality.

The only value, from that set, to make the original inequality false is the value x = 10.2

This is why the answer is choice 3.

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Side Note (extra optional info)

If we solve the given inquality for x, we get the following:

$8.9 - 0.3x \ge 0.8x$

$8.9 - 0.3x + 0.3x \ge 0.8x + 0.3x$

$8.9 \ge 1.1x$

$1.1x \le 8.9$

$\frac{1.1x}{1.1} \le \frac{8.9}{1.1}$

$x \le 8.09$

The value 8.09 is approximate

Since the solution set is x values that satisfy $x \le 8.09$ , this basically means any value smaller than 8.09 will work. Those values include: 0, 3.9 and 5.1. The value 10.2 is not smaller than 8.09 which is why it is excluded.