Write out the inequality equation clearly. For example:
3x + 6 > 8x + 4
Solve the equation to combine like terms. Follow the order of operations regarding how to manipulate and combine terms. You can easily remember the order of operations with the acronym PEMDAS, which stands for parentheses, exponents, multiplication and division, and then addition and subtraction. Using the example, first subtract 8x from both sides to get the x terms on the left side of the equation:
3x + 6 - 8x > 8x + 4 - 8x
Which leaves -5x + 6 > 4.
Next, subtract 6 from both sides to get the constant terms on the right side of the inequality sign:
-5x + 6 - 6 > 4 - 6
Which leaves -5x > -2.
Manipulate the problem to get x on one side of the inequality sign by itself. Again, adhere to PEMDAS. Continuing with the example, divide both sides by 5 to get x on the left side by itself:
-5x/5 > -2/5
Which leaves -x > -2/5.
Because you have -x, multiply both sides by -1 to convert -x into x:
-x (-1) > -2/5 (-1)
Which leaves x < 2/5. Note that the sign switched from greater-than to less-than, because whenever you multiply or divide both sides of the inequality by a negative, the sign changes.