Solve the inequality. Graph and check your solutions.
-15 > y - 3
To solve the inequality -15 > y - 3, we need to isolate the variable y.
First, we can add 3 to both sides of the inequality:
-15 + 3 > y - 3 + 3
-12 > y
Next, we can flip the inequality sign since we are multiplying or dividing by a negative number:
y < -12
To graph the solution, we can represent the inequality on a number line. We place an open circle on -12 and shade to the left, indicating that y is less than -12.
Checking a value, let's choose y = -13. Plugging this value back into the original inequality:
-15 > -13 - 3
-15 > -16
Since -15 is greater than -16, the inequality holds true for y = -13.
Therefore, the solution to the inequality is y < -12.
Graphically, this would look like:
<=======================>
-14 -13 -12 -11 -10
With an open circle at -12 and shaded to the left.
To solve the inequality -15 > y - 3, we will follow these steps:
Step 1: Add 3 to both sides of the inequality:
-15 + 3 > y - 3 + 3
Simplifying:
-12 > y
Step 2: Rearrange the inequality, with y on the left side:
y < -12
Now let's graph the solution on a number line:
Since y is less than -12, we will place an open circle on -12 and draw an arrow to the left.
-12•–––––––––––>
Now, let's check the solution by substituting a few values for y:
For example, let's substitute y = -13.
-15 > -13 - 3
-15 > -16
Since -15 is greater than -16, the inequality holds true.
Now let's substitute y = -11.
-15 > -11 - 3
-15 > -14
Since -15 is not greater than -14, the inequality does not hold true.
To solve the inequality -15 > y - 3, we need to isolate the variable y by performing algebraic operations.
Let's start by moving -3 to the other side of the inequality:
-15 + 3 > y - 3 + 3
Simplifying the equation:
-12 > y
Now we have isolated y on the right side of the inequality. This means that y is less than -12.
To graph this inequality, we draw a number line and mark -12 with an open circle (because y is less than, not equal to -12). Then we shade the region to the left of -12 since y is less than -12.
Finally, to check the solution, we can choose a value less than -12, such as -13, and substitute it back into the original inequality:
-15 > -13 - 3
Simplifying:
-15 > -16
Since this statement is true, we can conclude that -13 is a valid solution.
Therefore, the solution to the inequality is y < -12.