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3 years ago

|3x-11|=x+3 Write both solutions as equations on the same line separated by a comma.

Mathematics

1 answer:

Akimi4 [234]3 years ago

8 0

Answer:

x = 2, x = 7

Step-by-step explanation:

Given

| 3x - 11 | = x + 3

The absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, thus

3x - 11 = x + 3 or - (3x - 11) = x + 3

Solving both equations

3x - 11 = x + 3 ( subtract x from both sides )

2x - 11 = 3 ( add 11 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7

- (3x - 11) = x + 3

- 3x + 11 = x + 3 ( subtract x from both sides )

- 4x + 11 = 3 ( subtract 11 from both sides )

- 4x = - 8 ( divide both sides by - 4 )

x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

x = 7

| 3(7) - 11 | = | 21 - 11 | = | 10 | = 10

right side = 7 + 3 = 10 → both sides are equal thus x = 7 is a solution

x = 2

| 3(2) - 11 | = | 6 - 11 | = | - 5 | = 5

right side = 2 + 3 = 5 → both sides are equal thus x = 2 is a solution

The solutions are x = 2, x = 7

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3 years ago

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has under

Ann [662]

Answer:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

Step-by-step explanation:

Data given and notation

$\bar X=1.20$ represent the sample mean given

$\sigma = 0.14$ represent the population standard deviation

$n=49$ sample size

$\mu_o =1.25$ represent the value that we want to test

t would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean for the gasoline prices is lower than 1.25, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1.25$

Alternative hypothesis: $\mu < 1.25$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

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