Other than a no solution​ set, use interval notation to express the solution set and then graph the solution set on a number line.
2 x plus 4 less than 10


Let's solve the inequality \( 2x + 4 < 10 \).

### Step-by-Step Solution:

1. **Subtract 4 from both sides** to isolate the term with \( x \):
   \[
   2x + 4 - 4 < 10 - 4
   \]
   \[
   2x < 6
   \]

2. **Divide both sides by 2** to solve for \( x \):
   \[
   \frac{2x}{2} < \frac{6}{2}
   \]
   \[
   x < 3
   \]

### Interval Notation:
The solution set for \( x \) is all values less than 3, which can be expressed in interval notation as:
\[
(-\infty, 3)
\]

### Graph on a Number Line:
On a number line, this would be an open interval to the left of 3, meaning we don't include 3 (since the inequality is strict).

- Draw a number line.
- Place an open circle at \( x = 3 \) to indicate that 3 is not included.
- Shade everything to the left of 3 to represent all values less than 3.

Would you like me to graph this for you?

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### Related Questions:

1. How do you solve inequalities that involve multiplication or division by negative numbers?
2. What changes in the interval notation if the inequality was \( 2x + 4 \leq 10 \)?
3. How do you solve compound inequalities, such as \( 2x + 4 < 10 \) and \( x > 1 \)?
4. How would the solution change if the inequality was \( 2x + 4 > 10 \)?
5. What is the difference between strict and non-strict inequalities in interval notation?

**Tip:** Always remember, when dividing or multiplying by a negative number in an inequality, the inequality sign flips!

Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 2x + 4 < 10

Learn how to solve the linear inequality 2x + 4 < 10 and express the solution in interval notation. This step-by-step solution includes isolating the variable, solving the inequality, and graphing the result on a number line. Ideal for students in Grades 6-8 studying inequalities and interval notation.

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