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.

x

step-by-step explanation: