Question

solve the linear inequality for b and graph the answer in the number line. then write the solution in inequality notation.

b - 5 > 4

show your work here

hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

-15 -10 -5 0 5 10 15
toggle point toggle line

solution:

Explanation:

Step1: Add 5 to both sides

To solve \( b - 5 > 4 \), we add 5 to both sides of the inequality. This is based on the addition property of inequalities, which states that adding the same number to both sides of an inequality does not change the direction of the inequality sign. So, we have:
\( b - 5 + 5 > 4 + 5 \)
Simplifying both sides, we get:
\( b > 9 \)

Step2: Graph the solution on the number line

For the inequality \( b > 9 \), we use an open circle at 9 (because the inequality is strict, \( > \), not \( \geq \)) and draw an arrow to the right to represent all numbers greater than 9. Looking at the given number line, we need to adjust the toggle point to 9 (since currently it's at 0) and ensure the line is drawn to the right of 9.

Answer:

The solution to the inequality \( b - 5 > 4 \) is \( b > 9 \). The graph should have an open circle at 9 and an arrow pointing to the right. In inequality notation, the solution is \( \boldsymbol{b > 9} \).