Question

Hi! I just wanted to know may you please help me on knowing how to solve an inequality?

Answer 1

When given an inequality, we solve it as if we were solving an equation but there is one important consideration: If we divide or multiply by a negative number the inequality gets inverted.

Recall that to solve an equation we add, subtract, multiply, etc. to isolate the variable, in the case of inequalities we do the same process.

Example 1. x+58>36, to solve the inequality for x, we have to put the variable by itself on one side of the inequality, to do that we have to eliminate whatever is next to the variable, in the case 58 is adding, therefore, we must subtract it, but to not alter the inequality we do the same to both sides of the inequality.

Adding -58 to both sides of the inequality we get:

`\begin{gathered} x+58-58>36-58, \\ x>-22. \end{gathered}`

Therefore, the solution to this inequality is x>-22.

Example 2. -3x+3<4:

Adding -3 to both sides of the inequality we get:

`\begin{gathered} -3x+3-3<4-3, \\ -3x<1. \end{gathered}`

Dividing by -3 we get:

`\begin{gathered} (-3x)/(-3)>(1)/(-3), \\ x>-(1)/(3)\text{.} \end{gathered}`