# Inequality solve (x+1)/6<x-(3x-2)/4

• MHB
• karush
In summary, the conversation discusses the meaning of "inequality" in a mathematical context and how to solve a given inequality using algebra. It also mentions the purpose of solving inequalities and the specific rules and steps to follow when solving them.
karush
Gold Member
MHB
View attachment 9261
Ok a student sent this to me yesterday so want to answer without too many steps

I think the first thing to do is multiply every
term by 12

$2(x+1)<12x-3(3x-2)$
Expanding
$2x+2<12x-9x+6$

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That’s fine.

skeeter said:
That’s fine.
$\dfrac{x+1}{6}<x-\dfrac{3x-2}{4}$
Expanding
$2x+2<12x-9x+6$
Combine like terms
$2x+2<3x+6$
Subtract 2x from both sides
$2<x+6$
Subtract 6 from both sides
$-4<x$

Hopefully no typos

Last edited:

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

The first step in solving this inequality is to simplify the expressions on both sides of the inequality sign by combining like terms and distributing any coefficients.

## 2. How do I determine the critical values for this inequality?

The critical values for this inequality can be found by setting the expressions on both sides of the inequality sign equal to each other and solving for x. These values will divide the number line into different intervals.

## 3. Can I multiply or divide both sides of the inequality by a negative number?

Yes, you can multiply or divide both sides of the inequality by a negative number. However, you must remember to flip the direction of the inequality sign when doing so.

## 4. How do I graph the solution for this inequality?

To graph the solution for this inequality, plot the critical values on a number line and then determine which intervals satisfy the inequality. The solution will be represented by a shaded region on the number line.

## 5. Is there a specific order in which I should solve this inequality?

Yes, when solving an inequality, it is important to follow the order of operations, just like in solving an equation. Simplify the expressions on both sides of the inequality sign first, then isolate the variable on one side of the inequality, and finally, graph the solution and state the solution in interval notation.

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