Solve the inequality and graph the solution.

Question

7a+9<2

Answer 1

To solve the inequality \(7a + 9 < 2\), we can follow these steps:

1. Subtract 9 from both sides: \[ 7a + 9 - 9 < 2 - 9 \] This simplifies to: \[ 7a < -7 \]

2. Divide both sides by 7: \[ a < \frac{-7}{7} \] This simplifies to: \[ a < -1 \]

Now we have the solution \(a < -1\).

Graphing the Solution

To graph the solution on a number line:

• Draw a number line.
• Locate -1 on the number line.
• Use an open circle at -1 to indicate that -1 is not included in the solution (because the inequality is strict).
• Shade the line to the left of -1 to indicate all numbers less than -1.

Here's a textual representation:

<----(----|----)---->
       -2   -1    0

Where:

• The open circle at -1 indicates it's not included in the solution.
• The shaded area to the left of -1 indicates all values less than -1 are part of the solution.