Solve the inequality. Graph and check your solutions.
-12>y-3
To solve the inequality -12 > y-3, we can add 3 to both sides to isolate y:
-12 + 3 > y-3 + 3
-9 > y
So the solution to the inequality is y < -9.
To graph this inequality, we can draw a number line and shade all the values to the left of -9:
<------o---------|------------>
-10 -9 -8
Checking the solution, we can choose a value to the left of -9, such as -10:
-12 > -10-3
-12 > -13
This is true, so -10 is a valid solution.
To solve the inequality -12 > y-3, we need to isolate y.
First, let's add 3 to both sides of the inequality:
-12 + 3 > y - 3 + 3
Simplifying, we have:
-9 > y
Now, let's graph the solution on a number line. We represent -9 as a filled circle on -9 and draw an arrow to the left to indicate that all values less than -9 are solutions.
------------------●------------>
Finally, let's check our solution by substituting a value less than -9 into the original inequality. For example, let's try y = -10:
-12 > -10 - 3
-12 > -13
This statement is true, so the solutions for the inequality -12 > y-3 are all values less than -9.
To solve the inequality -12 > y - 3, we need to isolate the variable y.
First, let's start by adding 3 to both sides of the inequality:
-12 + 3 > y - 3 + 3
-9 > y
This inequality states that y is less than -9.
To represent this inequality graphically, we will draw a number line. We will mark a closed dot at -9 (since it is not included in the solution) and shade the region to the left of -9.
|
(---o---)
-9
So, the solution to the inequality -12 > y - 3 is y < -9.
To check our solution, we can substitute some values into the inequality and see if they satisfy it. For example, if we substitute y = -10 into the original inequality:
-12 > -10 - 3
-12 > -13
This is true, so -10 is a valid solution. We can also check y = -8:
-12 > -8 - 3
-12 > -11
This is also true, so -8 is a valid solution.
By graphing the inequality and checking the solutions, we can confirm that y < -9 is indeed the solution to the inequality -12 > y - 3.