Solve the inequality |6x + 2| < 10 and graph its solution.

Answers

Answer 1

Answer: This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3

Second part: when (6x + 2) is negative.

-(6x + 2) < 10   Divide both sides of inequality by -1 and change the sign.

(6x + 2) > -10
   6x + 2 > -10
   6x > -10 - 2
   6x > -12 Divide both sides by 6.
   x > -12/6
   x > -2.

Combined solution:   x < 4/3 and x > -2

-2 < x < 4/3.

Graph is a line on the number line between -2 and 4/3.

-2 and 4/3 are excluded from solution.

Related Questions

If the two lines 2x + y= 0 and y=3 are plotted on a typical xy coordinate grid, at which point will they intersect?Can someone point me in the direction of a vidoe to show how this is done
The graph of the function, f(x) = - 3x2 , opens which way up or down
Solve for x w=-2x+p/2
$3450 is invested into an account earning 2.27% interest for 5 years. Compounded monthly.
Sally sold 1000987 hot dogs 3 years how many will she sell in 6 years

At the zoo,there were 3 times as many monkeys than lions.Tom counted a total of 24 monkeys and lions.How many monkeys were there?

Answers

so monkeys/3=lions or monkeys=3(lions)
monkeys+lions=24
subsitute monkeys=3(lions) for monkeys in the second equation
3(lions)+lions=24
add like terms
4lions=24
divide both sides by 4
lions=6
subsitute lions=6 into second equation
monkeys+6=24
subtract 6 from both sides
monkeys=18

$3x-\ monkeys\nx-\ lions\n\n3x+x=24\n4x=24\ \ \ \ divide\ by\ 4\nx=6\n\n3x=18\n\nThere\ are\ 18\ monkeys\ and\ 6\ lions.$

Write an equation that is perpendicular to the line y = 2x + 13?

Answers

An equation can't be perpendicular to a line, but the graph of the equation can.

When that happens, we recall that the slopes of perpendicular lines are negative reciprocals.

One line is the graph of [ y = 2x + 13 ]. The slope of the line is 2 .
So the slope of a line perpendicular to it must be -1/2 .

The equation of a line perpendicular to it is: y = (-1/2 x) plus (any number).

The y-intercept of the perpendicular line doesn't matter. Only its slope does.

$k:\ y=m_1x+b_1\ \ \ and\ \ \ l:\ y=m_2x+b_2\n\nk\perp l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\n------------------------\n\nk:\ y=2x+13\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\n\n2\cdot m_2=-1\ \ \ \Leftrightarrow\ \ \ m_2=- (1)/(2) \n\nl:\ y=- (1)/(2) x+b_2\ \ \ and\ \ \ b_2\ \in\ R\n\nfor\ example:\n\ny=- (1)/(2) x,\ \ \ y=- (1)/(2) x+5 (1)/(7) ,\ \ \ y=- (1)/(2)x - √(13)\ ,\ ...$

Help please thank you. first answer choice is yes or no.
other answer choices are: 3 4 5 6

Answers

Hello there! Here are your answers:

Does Kerri's dot plot match the data in the tally table? No.

Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.

The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):

5 - classmates spent 3 hours at the park

3 - classmates spent 4 hours at the park

6- classmates spent 5 hours at the park

4 - classmates spent 6 hours at the park

I hope this was helpful and let me know if you need more help! :) Have a great day! :)

Answer:

the other guy is right

Step-by-step explanation:

-~- boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii laggy

How many metres in 187cm

Answers

1.87 meters are 187 centimeters. Hope it helped you if it helped please mark as the brainliest answer

It is 1.87 metres :)

Which is a subset of {1, 2, 4, 5, 6}?{0, 1, 2}
{3, 4}
{5, 6, 7}
{2, 6}

Answers

{2,6} is a subset of set {1, 2, 4, 5, 6} which is correct option (D).

What is a set?

A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.

What is a Subset?

A subset is defined as part of a given set subset (another set or the same set). The set notation to represent a set A as a subset of set B is written as A ⊆ B.

Given set as :

{1, 2, 4, 5, 6}

There are 2⁵ = 32 subsets

(which you know because there are 5 numbers in the set).

{},{1},{2},,{ 4},{ 5},{ 6},

{1,2},{1, 4},{1, 5},{1, 6}

{2, 4},{2, 5},{2, 6},

{ 4, 5},{ 4, 6},{ 5, 6},

,{1,2, 4},{1,2, 5},{1,2, 6}

,{1, 4, 5},{1, 4, 6},{1, 5, 6}

,{2, 4, 5},{2, 4, 6},{2, 5, 6}

,{ 4, 5, 6} {1,2, 4, 5, 6},

{1, 2, 4, 5, 6}

So, {2,6} is a subset of {1, 2, 4, 5, 6}

Thus they are both included in the set.

Hence, {2,6} is a subset of set {1, 2, 4, 5, 6}.

Learn more about Subset here:

brainly.com/question/23454979

#SPJ2

{2,6} because they are both in the first set

Walt made an extra $7000 last year from a part-time job. He invested part of the money at 10% and the rest at 7%. He made a total of $580 in interest. How much was invested at 7%?Select one:

Answers

We know that
Interest= PNR/ 100.
where P is the principal
R is the rate of Interest
N is the no of years the sum has been invested for.
Since N is not given we assume that to be 1
Therefore we have
10x /100 + (7000 -x)*7/100= 580

Multiplying both sides by 100
10x+(7000-x)*7 = 58000
simplifying
10x+ 49000 - 7x = 58000
3x = 58000-49000
3x = 9000
x= 3000
therefore the sum of money invested at 7% = 7000 - 3000 = 4000

Final answer:

Using the given conditions, we establish two equations. The first from the total invested amount which of 7000 dollars and the second from the total interest of $580. We solve the system of equations to find the value of x, which signifies the amount invested at 10%. The rest of the money (7000 - x) was invested at 7%.

Explanation:

To solve this problem, we need to set up two equations based on the information given. These equations can be set up with the following assumptions: let us denote the amount of money invested at 10% as x and at 7% as 7000 - x.

First equation would be derived from the total amount invested which was $7000, so x + (7000 - x) equals to 7000.
The second equation can be established from the total interest which was $580, so 0.10x + 0.07(7000 - x) equals to 580.

Solve the system of these two equations to find the value of x. The solution will yield the amount that was invested at 10%. The rest of the $7000, that is (7000 - x), was invested at 7%, which is what we're looking for.

Learn more about mathematical problem solving here:

brainly.com/question/32199704

#SPJ2

Other Questions

The formula for perimeter of a rectangle is given by p = 2l + 2w, where p = perimeter, l = length, and w = width. solve the formula for w.

A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.What is the child’s age for the outlier?

True or False: You can draw a quadrilateral with no parallel lines and at least one right angle.

TRICKY QUESTION: PLS HELP? If the side length of a square pyramid is tripled and the slant height is divided by 5, what would be the formula to find the modified surface area?