Question

consider the following linear inequality.
4n - 20 < -15 + 3n
step 2 of 2 : graph the solution set.
answer
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pressing the buttons will create an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed intervals, use the clear button. to indicate infinity or negative infinity, drag an open end point to the end of the number line.
← −∞ −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 ∞→

Explanation:

Step1: Solve the inequality \(4n - 20 < -15 + 3n\)

Subtract \(3n\) from both sides: \(4n - 3n - 20 < -15 + 3n - 3n\), which simplifies to \(n - 20 < -15\).

Step2: Isolate \(n\)

Add 20 to both sides: \(n - 20 + 20 < -15 + 20\), so \(n < 5\).

Step3: Graph the solution

On the number line, we have an open circle at 5 (since \(n < 5\), not \(n \leq 5\)) and an arrow pointing to the left (towards negative infinity) to represent all numbers less than 5.

Answer:

The solution set \(n < 5\) is graphed with an open circle at 5 and an arrow to the left on the number line. In interval notation, this is \((-\infty, 5)\).