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.