# Solving Inequality 4x-12≤6x+20

• MHB
• gazparkin
In summary, the conversation is about solving a linear equality and finding the value of x. The steps involve evening out the x's on both sides and dividing the remaining terms, but it is important to pay attention to the signs and inequality symbol to get the correct answer.
gazparkin
Hello,

I'm working on solving linear equalities (with equations) and can anyone help with the below question. I know the answer is -16, but I can't figure out the steps that gets it to this.

4x-12≤6x+20

Once I've evened out the x's on both sides and got this to 2x, I'm then left with -12 and +20, which leaves +8, divided by the remaining 2x, which leaves 4. This isn't correct though, so could anyone help me with the different stages on this.

Thank you!

Hello gazparkin.

gazparkin said:
Once I've evened out the x's on both sides and got this to 2x, I'm then left with -12 and +20, which leaves +8, divided by the remaining 2x, which leaves 4.
You’re on the right line, but when you move the $20$ from the RHS to the LHS, you should have $-20$, not $+20$.

gazparkin said:
The answer is not just -16. The answer involves $-16$, the variable $x$, and an inequality sign in between. It’s important to get the inequality sign right, or you won’t get any marks for the question.

## What is the first step in solving this inequality?

The first step in solving this inequality is to simplify both sides of the equation by combining like terms. In this case, we can combine the 4x and 6x terms to get 10x. This gives us the new inequality: 10x-12≤20.

## What is the next step after simplifying the inequality?

The next step is to isolate the variable on one side of the inequality. In this case, we can add 12 to both sides of the inequality to get 10x≤32.

## How do I solve for x in this inequality?

To solve for x, we need to get rid of the coefficient of 10. We can do this by dividing both sides of the inequality by 10. This gives us the solution x≤3.2.

## Is there a difference between solving for x and graphing the inequality?

Yes, there is a difference. Solving for x gives us a specific numerical solution, while graphing the inequality shows us all the possible values of x that make the inequality true. In this case, the graph would show a shaded region to the left of the vertical line x=3.2.

## What is the solution set for this inequality?

The solution set for this inequality is all real numbers less than or equal to 3.2. This can be written as (-∞, 3.2].

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