Question

integrated math 1 - unit 3

1. solve the inequality and graph its solution.

v - 1 < 3

Explanation:

Step1: Isolate the variable \( v \)

To solve the inequality \( v - 1 < 3 \), we add 1 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.

$$ v - 1 + 1 < 3 + 1 $$

Step2: Simplify both sides

Simplifying the left - hand side \( v-1 + 1=v \) and the right - hand side \( 3 + 1 = 4 \). So we get \( v<4 \).

For graphing the solution:

• Draw a number line.
• Locate the point 4 on the number line.
• Since the inequality is \( v < 4 \) (not \( v\leq4 \)), we use an open circle at 4 to indicate that 4 is not included in the solution set.
• Then, draw an arrow to the left of 4 to represent all the numbers less than 4.

Answer:

The solution to the inequality \( v - 1<3 \) is \( v < 4 \). The graph of the solution has an open circle at \( 4 \) on the number line with an arrow pointing to the left.