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tensa zangetsu [6.8K]
2 years ago
14

Solve |2x - 2| < 8

Mathematics
1 answer:
myrzilka [38]2 years ago
5 0

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-2|

For the Negative case we'll use -(2x-2)

For the Positive case we'll use (2x-2)

-(2x-2) < 8

Multiply

-2x+2 < 8

Rearrange and Add up

-2x < 6

Divide both sides by 2

-x < 3

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -3

Which is the solution for the Negative Case

(2x-2) < 8

Rearrange and Add up

2x < 10

Divide both sides by 2

x < 5

Which is the solution for the Positive Case

-3 < x < 5

( - 3,5)

One solution was found :

<h2> -3 < x < 5</h2>
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Answer:

A. Zero

Step-by-step explanation:

This would have no solution because when you try to solve the equation and simplify, the 4x's cancel out, leaving no variable and making the equation reduce to: -8=9 which is false, and therefore, this has no solution.

I hope this helps!

3 0
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Calculate the area of this parallelogram.
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Write the following as an inequality: y is no greater than 4 but more than –2.
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Step-by-step explanation:

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3 years ago
"Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given st
11111nata11111 [884]

Answer:

The error E = ± 4.04 %

Step-by-step explanation:

Solution:-

- The sample data is used to estimate the population proportion ( p ).

- The success p^ = success percentage = 40 %

- The confidence interval CI = 98%

- The sample size n = 800

- The margin of error E:

- The margin of error "E" for estimation of population proportion ( p ) is given by:

                          E = z-critical*\sqrt{\frac{p~ ( 1 - p~ )}{n} }

Where, Z-critical value is defined by the significance level:

                         P ( Z < Z-critical ) = α / 2

Where, α : Significance level

                          α = 1 - CI

                         P ( Z < Z-critical ) = (1 - 0.98) / 2

                         P ( Z < Z-critical ) = 0.01  

                         Z-critical = 2.33

- The error E of estimation is:

                        E = 2.33*\sqrt{\frac{0.4 ( 1 - 0.4 )}{800} }\\\\E = 0.04035

- The error E = ± 4.04 %

6 0
3 years ago
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