Question

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

$\mathbf{4}>\mathbf{b}\mathbf{+}\mathbf{1}$

Short answer

Solution set of inequality is $\mathbf{(}\mathbf{-}\infty \mathbf{,}\mathbf{3}\mathbf{)}$.

Solution set on number line is

Step-by-step solution

Step 1. Write properties of inequality.

Properties of inequalities are written in following table:

Step 2. Solve 4>b+1.

To solve given inequality, use subtraction and division properties of inequality. Subtract 1 from each side and do not change the sign of inequality.

$\begin{array}{c}4-1>b+1-1\\ 3>b\end{array}$

Thus, solution is $3>b$.

Step 3. Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than 3.

Write the solution set in interval notation.

$(-\infty ,3)$

Step 4. Graph the solution set.

Open circle on 3 shows this point is excluded in the solution set.