Question

Solve the inequality 4 - 4/3x < 16 + 1/4x, and graph the solution set on a number line. Write your answer and show your drawing in the space below.

please someone help. digital diagrams are good too.

Answer 1

`\sf x > -(144)/(19)`

Explanation:

Let's solve the given inequality:

`\sf 4 - (4)/(3)x < 16 + (1)/(4)x`

First, let's simplify the inequality:

`\sf 4 - (4)/(3)x < 16 + (1)/(4)x`

Multiply both sides by 12 to clear the denominators:

`\sf 12 \cdot \left(4 - (4)/(3)x\right) < 12 \cdot \left(16 + (1)/(4)x\right)`

Simplify:

`\sf 48 - 16x < 192 + 3x`

Now, let's isolate
`\sf x`:

`\sf 48 - 192 < 16x + 3x`

Combine like terms:

`\sf -144 < 19x`

Divide by 19 (remembering to reverse the inequality sign when dividing by a negative number):

`\sf x > -(144)/(19)`

Now, let's graph the solution on a number line. Since
`\sf x > -(144)/(19)`, the solution is all real numbers greater than
`\sf -(144)/(19)`.

For a number line: see Attachment

This line represents all real numbers greater than
`\sf -(144)/(19)`. The open circle at
`\sf -(144)/(19)` indicates that this value is not included in the solution set.

Therefore, the solution to the inequality is
`\sf x > -(144)/(19)`, and it can be represented graphically as shown in attachment.

Answer 2

The solution to the inequality expression 4 - 4/3x < 16 + 1/4x is x > -144/19

How to determine the solution to the inequality expression

From the question, we have the following parameters that can be used in our computation:

4 - 4/3x < 16 + 1/4x

When the like terms are collected, we have

- 1/4x - 4/3x < 16 - 4

Evaluate the like terms

This gives

- 1/4x - 4/3x < 12

Multiply through by 12

-3x - 16x < 144

So, we have

-19x < 144

Divide both sides by -19

x > -144/19

Hence, the solution is x > -144/19