Solve the inequality and graph it.
4(x-3)-6>18
You MUST show your work and graph your solution
To solve the inequality 4(x-3) - 6 > 18, let's simplify it step by step:
4(x-3) - 6 > 18
4x - 12 - 6 > 18 [Distribute the 4 to both terms inside the parentheses]
4x - 18 > 18 [Combine like terms]
Next, let's isolate the variable by adding 18 to both sides of the inequality:
4x - 18 + 18 > 18 + 18
4x > 36
Now, divide both sides by 4 to solve for x:
(4x)/4 > 36/4
x > 9
So the solution to the inequality is x > 9.
To graph the solution, we represent all values greater than 9 on a number line. We put an open circle at 9 to indicate that 9 is not included in the solution, and draw an arrow to the right to represent all the values greater than 9.
Here is the graph of the solution:
<IMG SRC="https://www.foolproofmath.com/wp-content/uploads/2021/04/graph2.png">