Solve the inequality. Graph and check your solutions.

Question

two sevenths plus a greater than or equals minus five sevenths
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Part 1
a
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less than
greater than
greater than or equals
less than or equals
  
enter your response here
​(Simplify your​ answer.)

Answer 1

To solve the inequality \( \frac{2}{7} + a \geq -\frac{5}{7} \), we will isolate \( a \).

1. Start with the inequality: \[ \frac{2}{7} + a \geq -\frac{5}{7} \]

2. Subtract \( \frac{2}{7} \) from both sides: \[ a \geq -\frac{5}{7} - \frac{2}{7} \]

3. Combine the fractions on the right side: \[ -\frac{5}{7} - \frac{2}{7} = -\frac{5 + 2}{7} = -\frac{7}{7} = -1 \]

4. The inequality now reads: \[ a \geq -1 \]

Part 1 - Your answer is: \[ a \text{ is greater than or equal to } -1 \]

Graphing the solution

On a number line, we would represent this solution as follows:

• Draw a solid circle at -1 (to indicate that -1 is included in the solution set).
• Shade to the right to indicate all numbers greater than -1.

Checking your solution

To check:

• Pick a value greater than -1, say \( a = 0 \): \[ \frac{2}{7} + 0 = \frac{2}{7} \] \[ \frac{2}{7} \geq -\frac{5}{7} \text{ (True)} \]

• Pick a value less than -1, say \( a = -2 \): \[ \frac{2}{7} - 2 = \frac{2}{7} - \frac{14}{7} = -\frac{12}{7} \] \[ -\frac{12}{7} \geq -\frac{5}{7} \text{ (False)} \]

The solution \( a \geq -1 \) is verified as correct.