This is an inequality expression. As you solve algebraic expressions solve this expression also the same way. You want to solve the inequality for the variable x, so your objective is to keep the variable on one side of the inequality. So, get rid of 4 on the left hand side.
1. Since it is -4 on the left hand side you add a + 4 on both the side of the ineqaulity as per the fact family concept. This will nullify the 4 on the left hand side and will add a 4 on the right side.
3x - 4 + 4 > 11 + 4
Now the inequality becomes
3x > 15
Now you want to get rid of 3 and you know that 3 is multiplied by x so as per the fact family concept we will go with dividing 3 on both the sides of inequality.
Inequality will look like this
(3/3)x > (15/3)
Finally, you get x > 5 (answer).
Now , if you want to graph this on the number line then follow these steps
- Draw a number line.
- Then locate the number 5 on the number line.
- Since, there's an > symbol you will put an open circle on number 5. Open circle indicates that number 5 is not included in the answer.
- Shade the number line greater than 5, and that's your answer for graphing.
To check your work, pick any number greater than 5, and not 5 and substitute for x in the original inequality. If the result is TRUE your answer is right.
For example: Let's take x = 6
3x - 4 > 11 (original inequality)
3 * 6 - 4 > 11 (substitute value of x)
18 - 4 > 11
14 > 11 (TRUE)
Also, for the fact family I mentioned above
when expression is in addition you subtract and vice versa
when expression is in multiplication you divide and vice versa
I hope this might help you. Good luck.