Question

can someone please help me with this question?

Solve the inequalities for x, and match each solution to its number line graph.

Answer 1

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.

Answer 2

The correct match of the solution of inequalities with its number line graph is:

• 1 : B
• 2: A
• 3 : C
• 4 : D

What is number line graph?

Number line graph is a method of representing numbers and integers over a graph. Representing a number on a number line is similar to representing a number on a graph.

The place at which the number occurs on the number line is highlighted with a dot.

In case when the inequality consists of greater than or less than sign, it is represented we need to draw a dot and then initiate a line based on the sign.

The solution of the first inequality can be calculated as follows:

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

$\rm \dfrac{1}{3} x + 2 \leq \dfrac{5}{2}$

On solving the equation we get:

$\rm x \leq 1.5$

The graph for the solution will be the one pointing 1.5 and showing a backward arrow from the same since the value of x is equal to or less than 1.5. The graph B hence is the correct match.

Similarly for inequality 2, the value of x will be:

2 times a number x is added to 4, which is less than 1

$\rm 2x + 4 <$ 1

On solving for the value of x we get:

x < -1.5

To graph the solution we will place an empty dot on -1.5 since the value of x cannot be -1.5, it is less than -1.5 therefore the line will move in backward direction from -1.5. Graph A is the correct match.

Similarly the value of x for inequality 3 is:

$\rm x > -1.5$

x > -1.5

The graph look like, an empty dot on -1.5 and the arrow moving forward. Graph C is the correct match.

And for inequality 4, the value of x will be:

x > -2.5 , therefore the graph will point towards -2.5 and then move forward. Graph D is the correct match.

Learn more about number line graph here:

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