Solve the inequality. Write the solution in set-builder notation.
-4x-11>-31
To solve the inequality -4x - 11 > -31, we can start by adding 11 to both sides:
-4x > -31 + 11
Simplifying the right side:
-4x > -20
Next, we can divide both sides by -4. Remember that when you divide an inequality by a negative number, the direction of the inequality sign needs to be flipped:
x < -20 / -4
Simplifying the right side:
x < 5
Therefore, the solution in set-builder notation is:
{x | x < 5}
To solve the inequality -4x - 11 > -31, we'll follow these steps:
Step 1: Add 11 to both sides of the inequality:
-4x - 11 + 11 > -31 + 11
-4x > -20
Step 2: Divide both sides of the inequality by -4 (remember to flip the inequality sign when dividing by a negative number):
(-4x) / -4 < (-20) / -4
x < 5
Therefore, the solution to the inequality is x < 5.
Now, let's express this solution in set-builder notation. In set-builder notation, the solution can be written as:
{x | x < 5}
This notation means "the set of all x such that x is less than 5."
To solve the inequality -4x - 11 > -31, we will isolate the variable x.
Step 1: Add 11 to both sides of the inequality:
-4x - 11 + 11 > -31 + 11
-4x > -20
Step 2: Divide both sides of the inequality by -4. Note that when dividing by a negative number, we need to flip the inequality sign:
(-4x)/-4 < (-20)/-4
x < 5
The solution to the inequality x < 5 can be written in set-builder notation as:
{x | x < 5}