Question

solve the following inequality. graph the solution set and write it in interval notation. 4x<3x + 8
choose the graph of the solution set
a. <graphical representation with arrow and number - 5, 0, 8, 15> b. <graphical representation with arrow and number - 5, 0, 5, 15> c. <graphical representation with arrow and number - 5, 0, 7, 15> d. <graphical representation with arrow and number - 5, 0, 10, 15> e. <graphical representation with arrow and number - 5, 0, 15> f. <graphical representation with arrow and number - 5, 0, 15>
select the correct choice below and, if necessary, fill in the answer - box to complete your choice
a. the solution set is
(type your answer in interval notation.)
b. the solution set is ∅

Explanation:

Step1: Isolate the variable x

Subtract 3x from both sides of the inequality \(4x<3x + 8\). We get \(4x-3x<3x + 8-3x\), which simplifies to \(x<8\).

Step2: Determine the graph

The inequality \(x < 8\) represents all real - numbers less than 8. On a number line, we have an open circle at 8 (because 8 is not included in the solution set) and an arrow pointing to the left.

Step3: Write in interval notation

In interval notation, the solution set is \((-\infty,8)\).

Answer:

A. The solution set is \((-\infty,8)\)
The graph of the solution set is A (an open - circle at 8 and an arrow pointing to the left).