Question

1. solve the inequality and graph its solution. -7 + x ≥ -8

Explanation:

Step1: Isolate the variable x

To solve the inequality \(-7 + x \geq -8\), we add 7 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.

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Step2: Graph the solution

To graph the solution \(x\geq - 1\) on a number line:

• Draw a number line.
• Locate the point \(-1\) on the number line.
• Since the inequality is "greater than or equal to", we use a closed circle (filled - in dot) at \(-1\) to indicate that \(-1\) is included in the solution set.
• Then, draw an arrow to the right of \(-1\) to show that all numbers greater than \(-1\) are also part of the solution set.

Answer:

The solution to the inequality is \(x\geq - 1\). The graph has a closed circle at \(-1\) and an arrow pointing to the right.