Question

Solve for x : 10x + 15 < 25 +5x

Answer 1

Solving inequalities is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here if the coefficient in front of x is positive when you divide!

1) Start by isolating the variable x. Since I don't want to divide by a negative number (you can if you want to!), I'll be subtracting 5x from both sides. I will also subtract 15 from both sides:

`10x + 15 \ \textless \ 25 +5x\\ 5x \ \textless \ 10`

2) Divide both sides by 5 to get the inequality for x:

`5x \ \textless \ 10\\ x \ \textless \ 2`

Your final inequality is x < 2.

Answer 2

`10x+15\ \textless \ 25+5x`

This is the inequality that is given. We are going to solve for the values of x that will satisfy this inequality.

To do so, we will have to isolate x on one side of the inequality with the number on the other side. This can be achieved by adding, subtracting, multiplying, or dividing both sides of the inequality by certain values.

Let's first subtract both sides by 5x.


`10x+15-5x\ \textless \ 25+5x-5x`


`5x+15\ \textless \ 25`

Now, let's remove the "15" on the left side so it can be possible to isolate x.
Subtract 15 from both sides.


`5x+15-15\ \textless \ 25-15`


`5x\ \textless \ 10`

Now, divide both sides by 5. When multiplying/dividing an inequality by a negative number, the inequality sign would have to be reversed. In this case, we are dividing by a positive number, so we will not have to reverse the inequality symbol.


`5x / 5 \ \textless \ 10 / 5`


`x\ \textless \ 2`

That is the solution to this inequality.

I hope you found this useful! If you have any further questions about this, feel free to comment and I'll be happy to get back to you! :)