Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

1. A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
2. A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
3. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
4. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right. (PICK 1,,2,3,4)

Question

31-07-2024
Mathematics

Answered

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

1. A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
2. A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
3. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
4. A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right. (PICK 1,,2,3,4)

Answer :

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cheesewhiz12378 cheesewhiz12378 · Answer 1 · 2024-07-31T01:21:16-04:00

Answer:

The correct answer is B, or 2: A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Step-by-step explanation:

To solve the inequality 3(8 – 4x) < 6(x – 5), follow these steps:

First, distribute the 3 into (8 - 4x) and the 6 into (x - 5):

[tex]24 - 12x < 6x - 30[/tex]

Next, add 12x to both sides to get all x terms on one side

[tex]24 < 18x - 30[/tex]

Then, add 30 to both sides to get constants on the other side:

[tex]54 < 18x[/tex]

Then, divide both sides by 18 to solve for x:

[tex]\frac{54}{18} < \frac{18x}{18}[/tex]

Simplifying:

[tex]3 < x[/tex]

From this equation, it is seen that x is greater than 3. On a number line, this is represented by an open circle at 3 with a line extending to the right, indicating all numbers greater than 3.

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