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IgorLugansk [536]
1 year ago
7

How do you solve a linear inequality and graph on a number line?

Mathematics
1 answer:
tiny-mole [99]1 year ago
5 0

This is very similar to solving linear equations except for one thing, If we multiply or divide by a negative number, we must flip the inequality sign.

<h3>What is linear inequality?</h3>

In mathematics, inequality occurs when a non-equal comparison is made between two mathematical expressions or two numbers. In general, inequalities can be either numerical inequality or algebraic inequality or a combination of both.

To better understand it, let's examine the example.

2x - 5 < 3

So, when we solve, let's just consider the inequality sign like a regular equal sign.

Let's start by adding 5 to each sides.

2x - 5 + 5 < 3 + 5  

To find the value of x , we must divide  it by two.

2x/2 <8/2

And the final result is x= 4.

This is our answer.

So if we need to graph it, let’s draw a number line and draw an open circle at 4. Open circle because x is not equal to 4. Then make an arrow going to the left.

to know more about linear inequality and graph:

brainly.com/question/21103162

#SPJ4

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That funky circle in the middle is the composition of the function. It asks you to take a function as an input and to yield an output that's another function. It's one of the five function operations, along with adding, subtracting, multiplying, and dividing.

When you compose, you might find the notation w(u(x)) easier to understand. It's saying evaluate u then evaluate w.

For our functions, the compositions are:

u(w(x)) = u(2x²) = -(2x²) - 2 = -2x² - 2

w(u(x)) = w(-x - 2) = 2(-x - 2)² = 2(x² + 4x + 4) = =2x²+ 8x +8

Now we evaluate each composition at 4.

u(w(4)) = -2(4²) - 2 = -2(16) - 2 = -32 -2 = -34

w(u(4)) = -2(2²) +8(2) + 8 = -2(4) + 16 + 8 = -8 + 16 + 8 = 16.

Thus, u(w(4)) = -34 and w(u(4)) = 16.

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