MATHEMATICS MIDDLE SCHOOL

What is the solution to this inequality
2(x - 4 ) < 5x + 4

Answers

Answer 1

Answer:

Answer:

x<4

Step-by-step explanation:

-Simplify the arithmetic

-Group all x terms on the left side of the equation

-Group all constants on the right side of the equation

-Isolate the x.

-Solution on a coordinate plane

x ≤ -11, Yes. The solution set include -11.

Step-by-step explanation:

$x+4\leq(1)/(2)(x-3)\qquad\text{multiply both sides by 2}\n\n2x+8\leq1(x-3)\n\n2x+8\leq x-3\qquad\text{subtract 8 from both sides}\n\n2x\leq x-11\qquad\text{subtract x from both sides}\n\n\boxed{x\leq-11}$

a catalog store has 6% of its orders returned for a refund the owner predicts that a new candle will have 812 returns out of the 16824 sold do you agree with this predection? explain

Answers

No, because the 6% of the 16824 candles is 1009.20 and the owner didn't do anything, his math was way off

6% percent of 16842 is 1009.44. The predicted amount is 812. This is a reasonable estimation, so I agree with the prediction.

Max delivers 8,520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in 2 months? Explain your steps.Can you help me and explain this question... Thanks!

Answers

So there are 12 months in a year and he delivers 8,520 in that time. You must divide 8,520 by 12 which gives you how many he delivers in one month. 8,520/12=710. You are looking for two months so you should then multiply 710 by two giving you how much he delivers in 2 months.
710*2=1,420
Max delivers 1,420 pieces of mail in two months

An equation is shown below: 4(2x − 3) = 4 Part A: What is the solution to the equation above? Show your work using inverse operations. (5 points) Part B: Check using substitution to make sure your answer is correct. (5 points)

Answers

Answer:

The solution of the given equation is x = 2.

Step-by-step explanation:

The given linear equation is,

$4(2x-3)=4$

At first, we will eliminate '4' from the LHS by dividing both sides i.e., LHS and RHS by 4 because '4' is present in multiplication with the term containing unknown in LHS.

So, dividing both sides by '4', we get

$(4(2x-3))/(4) = (4)/(4)$

$\implies 2x - 3 = 1$

Our next step will be to eliminate '3' from the LHS that is being subtracted from the term containg unknown variable. For this, we will add '3' on both sides of the above obtained equation.

So, adding '3' on both sides, we get

$2x - 3 + 3 = 1 + 3$

$\implies 2x = 4$

Now, we will eliminate '2' from the LHS that is in multiplication with the unknown variable 'x'.

For this, we will divide both sides of the above obtained equation by '2'.

So, dividing both sides by '2', we get

$(2x)/(2)=(4)/(2)$

$\implies x = 2$

CHECKING :

For this, we will substitute x = 2 in the LHS of the given equation and then check whether it is equal to RHS or not.

LHS = 4(2x - 3)

= 4(2 × 2 - 3)

= 4(4 - 3)

= 4 × 1

= 4

= RHS

So, the solution of the given equation is x = 2.

Answer:

see explanation

Step-by-step explanation:

(A) Given

4(2x - 3) = 4 ( divide both sides by 4 )

2x - 3 = 1 ( add 3 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

(B)

As a check substitute x = 2 into the left side of the equation and if equal to the right side then it is the solution.

4(2(2) - 3) = 4(4 - 3) = 4(1) = 4 = right side

Hence x = 2 is the solution

A study was done to investigate the population of polar bears over time. The correlating linear model is shown below, where x represents the number of years after 1955, and y represents the number of polar bears. Interpret the y-intercept.y = 5,000 + 500x

A. There were 10,000 polar bears in 1955.
B. There were 1,000 polar bears in 1955.
C. There were 5,000 polar bears in 1955.
D. There were 500 polar bears in 1955.

Answers

$y\ itercept\ is\ for\ x=0\n\ny=5000+500x\ \ \ | substitute\ x=0\n\ny=5000+500*0\ny=5000\n\nAnswer\ is\ C.$

Final answer:

The y-intercept represents the number of polar bears in 1955 and its value is 5,000.

Explanation:

The y-intercept of the given linear model, y = 5,000 + 500x, represents the starting value of y when x is 0. Since x represents the number of years after 1955, when x is 0, it corresponds to the year 1955. Therefore, the y-intercept represents the number of polar bears in 1955. In the given model, the y-intercept is 5,000. So, the correct interpretation is that there were 5,000 polar bears in 1955.