Question

Solve the inequality and graph the solution on the line provided.
2, x, minus, 2, is less than, 0
2x−2<
0
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 1

Solve the inequality and graph the solution on the line provided.
minus, 70, minus, 6, x, is less than or equal to, minus, 112
−70−6x≤
−112
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 2

To solve the inequality \( 2x - 2 < 0 \):

1. **Isolate \( x \)**:
\[
2x - 2 < 0
\]
Add 2 to both sides:
\[
2x < 2
\]
Now divide both sides by 2:
\[
x < 1
\]

Now, the solution in inequality notation is:
\[
x < 1
\]

2. **Graphing the Solution**:
On the number line, you would represent the solution \( x < 1 \) by placing an open circle at 1 to indicate that 1 is not included in the solution, and shading the line to the left of 1 to indicate all numbers less than 1 are included in the solution.

Here’s how you would represent it:

```
<----(----------)---->
0 1
```

- The open parenthesis ( indicates that 1 is not included in the solution.
- The shading to the left indicates all numbers less than 1 are included.

Answer 3

To solve the inequality \( -70 - 6x \leq -112 \):

1. **Isolate \( x \)**:
First, add 70 to both sides of the inequality:
\[
-6x \leq -112 + 70
\]
Simplifying the right-hand side:
\[
-6x \leq -42
\]

2. **Divide by -6**:
When dividing or multiplying both sides of an inequality by a negative number, you must flip the inequality sign:
\[
x \geq \frac{-42}{-6}
\]
Simplifying:
\[
x \geq 7
\]

Now the solution in inequality notation is:
\[
x \geq 7
\]

3. **Graphing the Solution**:
On the number line, you would represent the solution \( x \geq 7 \) by placing a closed circle at 7 to indicate that 7 is included in the solution, and shading the line to the right of 7 to indicate all numbers greater than or equal to 7 are included in the solution.

Here’s how you would represent it:

```
<----[----------)---->
6 7
```

- The square bracket [ indicates that 7 is included in the solution.
- The shading to the right indicates all numbers greater than or equal to 7 are included.