Solving Inequalities: Finding the Value of x in 8x-6>12+2x

Inequalities can be a challenging aspect of mathematics, but they are an important one to master. One type of inequality that you may encounter is finding the value of x in an equation such as 8x-6>12+2x.

To solve this type of inequality, you need to isolate the variable (in this case, x) to one side of the equation. Start by subtracting 2x from both sides of the equation:

8x – 2x – 6 > 12

Simplify by combining like terms:

6x – 6 > 12

Next, add 6 to both sides of the equation:

6x > 18

Finally, divide both sides by 6:

x > 3

So the solution to the inequality 8x-6>12+2x is x > 3.

It’s important to remember that if you multiply or divide both sides of the inequality by a negative number, the direction of the inequality symbol must be reversed. For example, if the original inequality was -8x-6>12+2x, you would start by adding 8x to both sides:

-6 > 12 + 10x

Then subtract 12 from both sides:

-18 > 10x

Divide both sides by -10, remembering to reverse the inequality symbol:

x < -1.8 In summary, solving inequalities can be tricky, but it's all about isolating the variable and keeping track of the direction of the inequality symbol. With practice and patience, you can master this important math concept.

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