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natima [27]
3 years ago
13

3x-7>8 and -3x ≥-36 solve the inequality

Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

Good evening,

Answer:

x > 5

x ≤ 12

Step-by-step explanation:

Visualize as if the inequality symbols are equal signs and then solve it as you would for a normal equation, note if you divide by two negative numbers at all you then switch the sign.

On a number line, an inequality sign without the “equal to” is plotted with an open circe.

An inequality sign, with the “equal to” is plotted with a closed circle.

3x - 7> 8

Add seven on both sides, we do this because we want to eliminate the 7 from one side.

3x > 15

Divide both sides by 3, we do this because you want to get rid of the 3 from x.

x > 5

As for the second inequality.

Divide both sides by -3, as I mentioned earlier switch the side since we are dividing by two negative numbers.

x ≤ 12

For the greater than inequality x > 5, plot a open circle on 5 and draw the line going to the right.

For the less than or equal to inequality x ≤ 12, plot a closed cirlce on 12 and draw the line going to the left.

A unique trick is to graph the line based on the direction (right or left) the inequality symbol is pointing to.

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Answer:

We have the sentence:

"X by the power of 5 times y to the power of 6 over 2 by the power of -2 times x by the power of 0times x by the power of 9"

Let's break it into parts.

"X by the power of 5 times y to the power of 6..."

This can be written as:

x^5*y^6

"...  2 by the power of -2 times x by the power of 0times x by the power of 9"

This can be written as:

2^(-2)*x^(0)*x^(9)

And we have the quotient between the first thing and the second thing, then the equation is:

\frac{x^5*y^6}{2^{-2}*x^0*x^9}

And any number by the power of 0 is equal to 1, then:

x^0 = 1, then we can rewrite the equation as:

\frac{x^5*y^6}{2^{-2}*x^9}

We can keep simplifying this.

We know that:

a^(-n) = (1/a)^(n)

Then:

2^(-2) = (1/2)^2 = 1/4

Then we get:

\frac{x^5*y^6}{2^{-2}*x^9} = \frac{x^5*y^6}{x^9}*4

And we also know that:

a^n/a^m = a^(n - m)

Then:

\frac{x^5*y^6}{x^9}*4 = 4*y^6*\frac{x^5}{x^9} = 4*y^6*x^{5 - 9} = 4*y^6*x^{-4} = \frac{4*y^6}{x^4}

And we can't simplify this anymore.

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What is the answer ​
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-5,5

Step-by-step explanation:

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