Question

solve the inequality and graph the solution.

$c + 7 < 10$

to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

number line from 0 to 10 with ticks at each integer

Explanation:

Step1: Subtract 7 from both sides

To solve the inequality \( c + 7 < 10 \), we subtract 7 from both sides of the inequality. This is based on the subtraction property of inequalities, which states that if we subtract the same number from both sides of an inequality, the direction of the inequality sign remains the same.

\[
c + 7 - 7 < 10 - 7
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( c+7 - 7=c \). Simplifying the right - hand side, \( 10 - 7 = 3 \). So we get the solution to the inequality:

\[
c < 3
\]

For graphing the solution:

• First, we identify the critical point, which is \( c = 3 \). Since the inequality is \( c<3 \) (not \( c\leq3 \)), we use an open circle at \( c = 3 \) on the number line to indicate that 3 is not included in the solution set.
• Then, we draw a ray (an arrow) starting from the open circle at 3 and pointing to the left (towards negative infinity or smaller values of \( c \)) to represent all the values of \( c \) that are less than 3.

Answer:

The solution to the inequality \( c + 7<10 \) is \( c < 3 \). The graph of the solution has an open circle at 3 and an arrow pointing to the left on the number line.