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1 year ago

Solve the inequality for x. Show each step of the solution.10x > 2(8x – 3) – 18

Mathematics

1 answer:

Luden [163]1 year ago

6 0

Answer: x<4

Given the inequality:

$10x>2(8x-3)-18$

We want to solve the inequality for x.

First, distribute the bracket on the right side of the inequality.

$\begin{gathered} 10x>2(8x)-2(3)-18 \\ 10x>16x-6-18 \\ 10x>16x-24 \end{gathered}$

Next, subtract 10x from both sides of the inequality.

$\begin{gathered} 10x-10x>16x-10x-24 \\ 0>6x-24 \end{gathered}$

Add 24 to both sides of the inequality.

$\begin{gathered} 0+24>6x-24+24 \\ 24>6x \end{gathered}$

Divide both sides of the inequality by 6.

$\begin{gathered} \frac{24}{6}>\frac{6x}{6} \\ 4>x \\ \implies x$

The solution to the inequality is x<4.

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7. Which property of polynomials says that the sum of two polynomials is also a polynomial?

vlabodo [156]

Answer:

Closure property

Step-by-step explanation:

The closure property of polynomials for addition says that, if we add any two polynomials , the result is also a polynomial.

For is

${x}^{2} + 2$

is a polynomial.

$x - 2$

is also a polynomial.

The sum of the two polynomials is

${x}^{2} + 2 + x - 2 = {x}^{2} + x$

The result:

${x}^{2} + x$

is also a polynomial.

4 0

2 years ago

H(x)=-|x|; Find h(6)

Alik [6]

Answer:

-6

Step-by-step explanation:

-|6|=-6

5 0

1 year ago

AX + B = C what is X equal to?

elena-14-01-66 [18.8K]

Answer:

x is a variable

Step-by-step explanation:

what happens an squared plus B equals C and what I want to do is solve for a so again what we want to do is when we're taking solver a we want to isolate the variable get the variable by itself so the data that need to look at well what is happening on my variable a well you can see me as being multiplied by X and it's being added by B so I need to undo those but we got to make sure we undo them in a certain upper certain order which we call the reverse order of operations which is like the order of operations but the reverse method meaning I'm gonna undo addition or subtraction first so you can see that since my variable a is being added by B I need to undo that by subtracting B and I'll use my subtraction property of equality that's going to now subtract a 0 and then these C minus B are not like terms so I'm going to write ax is equal to C minus B now I need to solve for a so I need to look at and say alright my a is being x over X so the inverse operation of multiplying is dividing by X so therefore have a equals C minus B divided by X now sometimes you could say alright that's correct but we could also divide this X into both of these terms and I'm going to rewrite this in a different form I could say a equals C over X minus B over X alright so what I'm doing is are just dividing those through

hope this helps

5 0

2 years ago

Answer the following 3 question(s) using the information from the scenario below.

finlep [7]

Answer:

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.

Step-by-step explanation:

Moonlight Hall:

Fixed cost = $1000

Cost per guest = $75

Cost of <em>'n' </em>guests = 75 $\times n$

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

$\Rightarrow 1000 + 75 \times n$

Riverside Hall:

Fixed cost = $1500

Cost per guest = $50

Cost of <em>'n' </em>guests = 50 $\times n$

Total cost of moonlight hall = Fixed cost + Cost of 'n' guests

$\Rightarrow 1500 + 50 \times n$

Hence, Answer 1:

a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: Coordinates of solution:

Option c. (20,2500) satisfies both the equation.

When there are 20 number of guests, the cost of both moonlight and riverside hall comes out to be 2500.

Moonlight Hall cost

$75 \times 20 + 1000\\\Rightarrow \$2500$

Riverside Hall cost

$50 \times 20 + 1500\\\Rightarrow \$2500$

Answer 3: c. When there are 20 guests attending the price is $2500.

The solution is done in Answer 2.

So,

Answer 1: a. Moonlight: C=75n+1000

Riverside: C=50n+1500

Answer 2: c. The solution coordinates are c. (20, 2500)

Answer 3: c. When there are 20 guests attending the price is $2500.

6 0

3 years ago

Substitution:(x=2y) (y=x-2)

GaryK [48]

Answer:

2=y

4=x

Step-by-step explanation:

x=2y

y=2y-2

add 2 to both sides

2+y=2y

subtract y from both sides

2=1y

2=y

5 0

2 years ago