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Artemon [7]
4 years ago
7

Solve for x: -3x - 6 < -5x - 2

Mathematics
1 answer:
Nonamiya [84]4 years ago
5 0

It is similar to an equation

-3x-6<-5x-2

-3x+5x<-2+6

2x<4

x<4/2

x<2

* when solving inequality problems you need to switch signs when you divide a side by a negative number.

Ex.

-3x-6<-5x-2

-6+2<-5x+3x

-4<-2x

When you divide -4 by -2, switch the lesser sign to greater sign.

-4/-2>x

2>x

Which gives you the same result either way.

x<2

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Use a number line to compare the numbers. Which shows the correct symbol to compare the numbers? 1.2 1 1/5
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For this case we must compare the following expressions:

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Define $g$ by $g(x)=5x-4$. If $g(x)=f^{-1}(x)-3$ and $f^{-1}(x)$ is the inverse of the function $f(x)=ax+b$, find $5a+5b$.
Slav-nsk [51]

Answer:

<h2>2</h2>

Step-by-step explanation:

Given g(x)=5x-4 and g(x)=f^{-1}(x)-3

Substituting g(x) =  5x-4 into the second equation we have;

5x-4 =  f^{-1}(x)-3

f^{-1}(x) = 5x-4+3

f^{-1}(x) = 5x-1

To get f(x), let us first make y to be equal  f^{-1}(x)

y = 5x-1

expressing x in terms of y to get f(x), we have;

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replacing y with x, we will have;

y = x/5 + 1/5

F(x) = x/5 + 1/5

Comparing x/5 + 1/5 with ax+b, a = 1/5 and b = 1/5

5a + 5b = 5(1/5)+ 5(1/5)

5a+5b = 1+1

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