Question # 01
Solve the inequality and sketch the solution on a coordinate line.
To solve an inequality and sketch the solution on a coordinate line, follow these steps:
1. Write down the inequality. For example, let's solve the inequality: 2x + 3 < 7.
2. Solve the inequality for x. In this case, subtract 3 from both sides of the inequality:
2x < 4.
3. Divide both sides of the inequality by the coefficient of x, which is 2:
x < 2.
4. Now, sketch the solution on a coordinate line. Start by drawing a number line and marking 0 as the reference point. Since the inequality is x < 2, we place an open circle on the number 2 to indicate that it is not included in the solution. Then, shade the region to the left of 2 to represent all values of x that satisfy the inequality.
5. The final step is to label the shaded region as the solution. In this case, you can write "x < 2" below the line.
Note: If the inequality had a "greater than" sign (>) instead of a "less than" sign (<), the shading would be on the right side of the number line.