Final answer:
To solve the inequality c + 4 > 7, subtract 4 from both sides to get c > 3. The solution set is all numbers greater than 3. Graphically, this is represented by an open circle at 3 with shading to the right, and checking a number greater than 3 confirms the solution is reasonable.
Step-by-step explanation:
To solve c +4> 7, the first step is to eliminate terms to simplify the expression. This can be done by subtracting 4 from both sides of the inequality:
c + 4 - 4 > 7 - 4
c > 3
The solution set for this inequality is all real numbers greater than 3, which can be written in interval notation as (3, \u221e).
Next, to graph this inequality, we draw a number line and place an open circle at the number 3 to indicate that 3 is not included in the solution set. Then, we shade the portion of the number line that extends to the right of 3, representing all numbers greater than 3.
To check the solutions, you can try substituting a number greater than 3 into the original inequality to see if it makes the inequality true. For example, if c=4, then:
4 + 4 > 7
8 > 7, which is true, so our solution is reasonable.