Solve for x and graph the solution on the number line below. the number line goes from -12 all the way to 12, please include how I should color the number line, 5x-15≤10, share the Inequality Notation as well

Answer 1

To solve the inequality \(5x - 15 \leq 10\), follow these steps:

Step 1: Isolate \(x\)

1. Start by adding 15 to both sides: \[ 5x - 15 + 15 \leq 10 + 15 \] \[ 5x \leq 25 \]

2. Next, divide both sides by 5: \[ \frac{5x}{5} \leq \frac{25}{5} \] \[ x \leq 5 \]

Step 2: Express the solution in inequality notation

The solution can be written as: \[ x \leq 5 \]

Step 3: Graph the solution on the number line

1. The solution indicates that \(x\) can take any value up to and including 5.
2. On the number line, you would draw a closed circle (or filled circle) at 5 to indicate that 5 is included in the solution set.
3. Shade the portion of the number line to the left of 5 to represent all numbers less than or equal to 5.

Number Line Representation

If you visualize the number line from -12 to 12, it will look like this:

-12  -11   -10   -9   -8   -7   -6   -5   -4   -3   -2   -1    0    1    2    3    4    5    6    7    8    9   10   11   12
  •----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----•=============================
                                                                       ^   |
                                                                       5   |

Note on Coloring:

• Coloring the Number Line: Starting from -12 up to 5 (including 5), shade the area to indicate all values less than or equal to 5. The part of the number line greater than 5 should not be shaded.

Summary:

• Inequality Notation: \(x \leq 5\)
• Number Line Graph: Closed circle at 5 with shading to the left of 5.