Can someone me with this question? solve the inequalities for x, and match each solution to its number line graph.

Answers:

Statement 1 is matched with line graph B.

Statement 2 is matched with line graph A.

Statement 3 is matched with line graph C.

Statement 4 is matched with line graph D.

Work:

1)

The sentence states, "1/3 of a number x is added to 2, which is at most 5/2."

This sentence can be translated to the following equation:

(1/3)x + 2 ≤ 5/2

Subtract two from both sides. Convert the fraction on the right side to a decimal:

5 / 2 = 2.5

2.5 - 2 = 0.5

(1/3)x ≤ 0.5

Multiply both sides by 3 to get rid of the fraction on the left side:

x ≤ 1.5

x is at most 1.5. This means that x can equal 1.5, so this will be graphed with a full dot at 1.5 with the line going left.

2)

The sentence states, "2 times a number x is added to 4, which is less than 1."

This sentence can be translated to the following equation:

2x + 4 < 1

Subtract 4 from both sides:

2x < -3

Divide both sides by 2 to get x by itself:

x < -3/2, or x < -1.5

x is less than -1.5. Because it cannot equal -1.5, it will be graphed with an empty dot at -1.5 with the line going left.

3)

The sentence states, "7/10 added to a number x is greater than -4/5".

This sentence can be translated to this equation:

x + 7/10 > -4/5

Convert the fractions into decimals:

7 / 10 = 0.7

-4 / 5 = -0.8

x + 0.7 > -0.8

Subtract 0.7 from both sides to get x by itself:

x > -1.5

x is greater than -1.5. Because x cannot equal -1.5, this will be graphed with an empty dot at -1.5 with the line going right.

4)

The sentence states, "2 times a number is subtracted from 3, which is at most 8."

This sentence can be translated to the equation:

3 - 2x ≤ 8

Add 2x to both sides:

3 ≤ 2x + 8

Subtract 8 from both sides:

-5 ≤ 2x

Divide both sides by 2 to get x by itself:

-5/2 ≤ x

Convert the fraction into a decimal:

-5 / 2 = -2.5

-2.5 ≤ x

x is greater than or equal to -2.5. This means that there will be a full dot at -2.5 with the line pointing right.

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

first you will have to convert 3/4 into a decimal

which is .75

then you will have to divide 1.5 by .75

which is 2

no you have to divide