Find the solution set of the inequality, express the solution in set notation. -9y + 4 < - 7y -2 Show your work in vertical form.
To solve the inequality -9y + 4 < -7y - 2, we can first combine like terms on both sides of the inequality.
-9y + 4 < -7y - 2
Subtract -4 from both sides:
-9y + 4 - 4 < -7y - 2 - 4
Simplifying:
-9y < -7y - 6
Next, we can subtract -7y from both sides:
-9y + 7y < -7y - 6 - 7y
Simplifying:
-2y < -6 - 7y
Now, we can combine like terms again:
-2y + 7y < -6 - 7y + 7y
Simplifying:
5y < -6
Finally, we divide both sides by 5 to solve for y:
5y/5 < -6/5
Simplifying:
y < -6/5
The solution to the inequality is y < -6/5.
Expressing the solution in set notation, the solution set is:
{y | y is a real number and y < -6/5}
To solve the inequality -9y + 4 < -7y - 2, we need to isolate the variable y.
Step 1: Subtract 4 from both sides of the inequality:
-9y + 4 - 4 < -7y - 2 - 4
-9y < -7y - 6
Step 2: Add 7y to both sides of the inequality:
-9y + 7y < -7y - 6 + 7y
-2y < -6
Step 3: Divide both sides of the inequality by -2. Since we are dividing by a negative number, we flip the inequality:
(-2y)/(-2) > (-6)/(-2)
y > 3
So, the solution to the inequality is y > 3. We can express this solution in set notation as:
{y | y > 3}
To solve the inequality -9y + 4 < -7y - 2, we need to isolate the variable y.
First, let's move all the y terms to one side of the inequality by adding 7y to both sides:
-9y + 7y + 4 < -7y + 7y - 2
Simplifying this gives us:
-2y + 4 < -2
Next, let's move the constant term to the other side of the inequality by subtracting 4 from both sides:
-2y + 4 - 4 < -2 - 4
Simplifying further:
-2y < -6
Now, we can isolate y by dividing both sides of the inequality by -2. We have to remember that when we multiply or divide an inequality by a negative number, we need to flip the direction of the inequality symbol:
(-2y) / -2 > -6 / -2
Simplifying this yields:
y > 3
So the solution set for the inequality -9y + 4 < -7y - 2 is all real numbers y that are greater than 3. This is expressed in set notation as:
{ y | y > 3 }