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2 years ago

1x -8 < 2x + 1 What is the largest integer value that makes this inequality true

Mathematics

1 answer:

professor190 [17]2 years ago

7 0

Answer:

The largest integer value that makes the inequality true is 9.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

1x - 8 < 2x + 1

Step 2: Solve for x

Simplify: x - 8 < 2x + 1
[Subtraction Property of Equality] Subtract x on both sides: -8 < x + 1
[Subtraction Property of Equality] Subtract 1 on both sides: -8 < x
Rewrite: x > -8

∴ we see that any number x greater than -8 would work as a solution to the inequality. That would mean the next largest integer, 9, would be our answer.

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Topic: Algebra I

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Answer:

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Now we can calculate the p value with the following probability:

$p_v =2*P(t_{60}$

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Step-by-step explanation:

Information given

$\bar X_{1}=14$ represent the mean for sample 1 (younger)

$\bar X_{2}=20$ represent the mean for sample 2 (older)

$s_{1}=5$ represent the sample standard deviation for 1

$s_{f}=6$ represent the sample standard deviation for 2

$n_{1}=31$ sample size for the group 2

$n_{2}=31$ sample size for the group 2

t would represent the statistic

System of hypothesis

We want to test if that people under the age of forty have vocabularies that are different than those of people over sixty years of age, the system of hypothesis are:

Null hypothesis: $\mu_{1}-\mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}\neq 0$

The statistic is given by:

$t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

And the degrees of freedom are given by $df=n_1 +n_2 -2=31+31-2=60$

Replacing the info given we got:

$t=\frac{(14-20)-0}{\sqrt{\frac{5^2}{31}+\frac{6^2}{31}}}}=-4.28$

Now we can calculate the p value with the following probability:

$p_v =2*P(t_{60}$

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Step-by-step explanation:

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