Can someone please help me with this inequality problem
-3-8>(4x+8)-8
I have no idea how to solve this problem but I would like to learn. Can you be kind to show me the steps so that I can use this as an example problem for other problems. Thanks!
for the first few lines treat the > sign as if it were an = sign
-3-8>(4x+8)-8
-11 > 4x + 8 - 8
-4x > 11
Now when we multiply or divide by a negative, the inequality sign has to be reversed
so divide both sides by -4
x < -11/4
Of course! I'd be happy to help you with this inequality problem and explain each step along the way.
The given inequality is:
-3 - 8 > (4x + 8) - 8
To solve this inequality, we need to start by simplifying both sides. Let's work on each side of the inequality separately.
On the left side, -3 - 8 can be calculated as:
-3 - 8 = -11
So, the left side of the inequality becomes:
-11 > (4x + 8) - 8
Now, let's simplify the right side of the inequality.
(4x + 8) - 8 can be calculated as:
(4x + 8) - 8 = 4x
Therefore, the right side of the inequality becomes:
-11 > 4x
Now, we have the inequality:
-11 > 4x
To isolate the variable x, we need to divide both sides of the inequality by the coefficient of x, which is 4. However, note that dividing an inequality by a negative number will change the direction of the inequality symbol.
So, dividing both sides of the inequality by 4, we get:
-11 / 4 > 4x / 4
which simplifies to:
-11/4 > x
Therefore, the solution to the given inequality is:
x < -11/4
In interval notation, this can be written as:
(-∞, -11/4)
Remember, when working with inequalities, it's important to pay attention to changing the direction of the inequality symbol if you multiply or divide by a negative number.
I hope this explanation helps you understand the steps involved in solving this inequality problem. Feel free to ask any further questions!