Solve the inequality and graph the solution on the line provided.

Question

8, x, minus, 7, is greater than or equal to, minus, 39
8x−7≥
−39
Answer


Inequality Notation:
Number Line:

Answer 1

To solve the inequality \( 8x - 7 \geq -39 \), follow these steps:

1. Add 7 to both sides: \[ 8x - 7 + 7 \geq -39 + 7 \] This simplifies to: \[ 8x \geq -32 \]

2. Divide both sides by 8: \[ x \geq -4 \]

Solution

The final result is:

• Inequality Notation: \( x \geq -4 \)

Graphing on a Number Line

To graph the solution on a number line:

• Draw a number line.
• Mark the point \(-4\).
• Since the inequality is greater than or equal to (\( \geq \)), use a closed dot on \(-4\) to indicate that \(-4\) is included in the solution.
• Shade the line to the right of \(-4\) to represent all numbers greater than \(-4\).

Here's a textual representation of the graph:

<---|----|----|----|----|----|----|--->
    -5   -4   -3   -2   -1    0    1   
              ●====================>

In the above graph:

• The dot on \(-4\) represents that \(-4\) is included.
• The shaded line to the right indicates all values greater than \(-4\).