Question

Solve the inequality and graph the solution on the line provided. the line goes from -12 to 12, remeber to tell me how to shade it. -7-4x>1

Answer 1

Inequality Notation:

Answer 2

To solve the inequality \(-7 - 4x > 1\), follow these steps:

1. **Isolate the term with \(x\)**:
\[
-7 - 4x > 1
\]
Add 7 to both sides:
\[
-4x > 1 + 7
\]
Simplifying gives:
\[
-4x > 8
\]

2. **Divide by \(-4\)**:
Remember that when dividing or multiplying both sides of an inequality by a negative number, you must flip the inequality sign.
\[
x < \frac{8}{-4}
\]
So:
\[
x < -2
\]

The solution to the inequality is \(x < -2\).

### Graphing the solution:

- **Draw a number line from -12 to 12.**
- **Since the inequality is strict (<), use an open circle at -2** (indicating that -2 is not included in the solution).
- **Shade to the left of -2 (indicating all numbers less than -2 are included in the solution).**

This visual representation signifies that all values less than -2 satisfy the inequality.

Answer 3

The solution to the inequality you provided, \(-7 - 4x > 1\), in inequality notation is:

\[
x < -2
\]

In interval notation, this is represented as:

\[
(-\infty, -2)
\]

This means that \(x\) can take any value from negative infinity up to but not including \(-2\).