Solve the inequality. Graph and check your solutions.

Question

xplus6greater than1
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Part 1
xgreater than
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the inequality \( x + 6 > 1 \), you can follow these steps:

1. Subtract 6 from both sides: \[ x + 6 - 6 > 1 - 6 \]

   This simplifies to: \[ x > -5 \]

So the solution to the inequality is: \[ x > -5 \]

Graphing the Solution

To graph the solution on a number line:

• Draw a number line.
• Place a circle (open circle) at \(-5\) to indicate that \(-5\) is not included in the solution.
• Shade the line to the right of \(-5\) to show that all numbers greater than \(-5\) are included.

Checking Your Solution

To check the solution, you can choose a value that is greater than \(-5\) (for example, \(-4\)) and a value that is less than or equal to \(-5\) (like \(-5\) itself):

1. Check \(x = -4\): \[ -4 + 6 = 2 \] Since \(2 > 1\), it satisfies the inequality.

2. Check \(x = -5\): \[ -5 + 6 = 1 \] Since \(1 \not> 1\), it does not satisfy the inequality.

Therefore, the solution \(x > -5\) is verified as correct.