Solve the inequality. Graph and check your solutions.

minus16less thanyminus6
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Part 1
y

less than or equals
greater than
less than
greater than or equals
  
enter your response here
​(Simplify your​ answer.)

1 answer

It looks like you're trying to solve the inequality \(-16 < y - 6\). Let's work through it step-by-step.

Step 1: Solve the Inequality

To isolate \(y\) in the inequality, we will add 6 to both sides:

\[ -16 + 6 < y \]

This simplifies to:

\[ -10 < y \]

We can also write this as:

\[ y > -10 \]

Step 2: Graph the Solution

To graph this inequality, you would draw a number line.

  1. Place a mark at \(-10\).
  2. Since the inequality is \(y > -10\), you draw an open circle at \(-10\) (indicating that \(-10\) is not included in the solution).
  3. Shade the line to the right of \(-10\) to indicate all values of \(y\) that are greater than \(-10\).

Step 3: Check Your Solution

You can check the solution by substituting a value that satisfies \(y > -10\) and one that does not:

  • Test value \(y = 0\) (which is greater than \(-10\)):

    • Inequality: \(-16 < 0 - 6 \rightarrow -16 < -6\) (True)
  • Test value \(y = -11\) (which is not greater than \(-10\)):

    • Inequality: \(-16 < -11 - 6 \rightarrow -16 < -17\) (False)

The solution \(y > -10\) is valid.

Final Answer

The solution to the inequality is:

\[ y > -10 \]

Graphically represented as a number line with an open circle at \(-10\) and a shaded line to the right.