Solve the inequality and graph the solution.

Question

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7+6n<5

Answer 1

To solve the inequality \(-7 + 6n < 5\), follow these steps:

1. Add 7 to both sides of the inequality: \[ -7 + 6n + 7 < 5 + 7 \] Simplifying this gives: \[ 6n < 12 \]

2. Divide both sides by 6: \[ \frac{6n}{6} < \frac{12}{6} \] Simplifying this leads to: \[ n < 2 \]

Thus, the solution to the inequality is \(n < 2\).

To Graph the Solution:

• On a number line, draw an open circle at 2 (indicating that 2 is not included in the solution set).
• Shade the region to the left of 2 to indicate all values of \(n\) that are less than 2.

Here's a simple representation of the graph:

----o========================>
     2

In this representation:

• "o" at 2 represents an open circle, showing that 2 is not included.
• The line extending to the left shows all numbers less than 2 are included in the solution.