Question

solve the inequality and graph the solution.
( a + 1 > 8 )
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
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Explanation:

Step1: Subtract 1 from both sides

To solve the inequality \( a + 1>8 \), we subtract 1 from both sides of the inequality. This is based on the subtraction property of inequalities, which states that if we subtract the same number from both sides of an inequality, the direction of the inequality sign remains the same.

So, \( a + 1-1>8 - 1 \)

Step2: Simplify both sides

Simplifying the left - hand side: \( a+1 - 1=a \)

Simplifying the right - hand side: \( 8 - 1 = 7 \)

So we get \( a>7 \)

For graphing the solution:

• The endpoint is at 7. Since the inequality is \( a>7 \) (not \( a\geq7 \)), the endpoint at 7 is an open circle (to indicate that 7 is not included in the solution set).
• Then, we draw an arrow starting from the open circle at 7 and pointing to the right (because we want all values of \( a \) that are greater than 7).

Answer:

The solution to the inequality \( a + 1>8 \) is \( a>7 \). For the graph, plot an open circle at 7 and draw an arrow to the right.