Solve the inequality 12+4x>16 and graph the solution set.
4x>4
x>1
line through x=1, shade to the right
To solve the inequality 12 + 4x > 16, we will follow these steps:
Step 1: Begin by subtracting 12 from both sides of the inequality to isolate the term with the variable:
12 + 4x - 12 > 16 - 12
4x > 4
Step 2: Divide both sides of the inequality by 4 to solve for x:
4x/4 > 4/4
x > 1
So, the solution to the inequality is x > 1.
To graph the solution set, we will use an open circle to denote that the value 1 is not included in the solution, and draw an arrow to the right to represent all values greater than 1.
Here is how the graph should look like:
<=======o------->
1
Note that the open circle indicates that 1 itself is not part of the solution set as the inequality is strict (x > 1), meaning it is only satisfied for values greater than 1.