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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.

User Taylorsuk
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2 Answers

6 votes

Answer:


\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.

Solve the inequality 4 - 4/3x < 16 + 1/4x, and graph the solution set on a number-example-1
User Ahars
by
8.4k points
3 votes

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

Solve the inequality 4 - 4/3x < 16 + 1/4x, and graph the solution set on a number-example-1
User Clemens Helm
by
7.6k points

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