First, let's work on the left hand side of your inequality, the 5
This means, for instance, to see if it can be simplified at all.
<span>So, all-in-all, the left hand side of your inequality can be written as: 5Now, let's work on the right hand side of your inequality, the -8+x
<span>Because of the minus sign8 becomes - 8<span>The answer is -8</span><span>-8+x evaluates to -8+x</span><span>The right hand side of your inequality can be written as: -8+x</span><span><span>So with these (any) simplifications, the inequality we'll set out to solve is:
<span>5 ‹ -8+x</span>
Move the 5 to the right hand side by subtracting 5 from both sides, like this:
From the left hand side:
<span>5 - 5 = 0</span><span>The answer is 0</span><span>From the right hand side:
<span>-8 - 5 = -13</span></span></span><span>
Now, the inequality reads:
0 ‹ -13+x</span><span>Move the x to the left hand side by subtracting x from both sides, like this:
From the left hand side:
<span>The answer is -x</span></span><span>From the right hand side:
<span>x - x = 0</span></span><span>The answer is -13</span><span>
Now, the inequality reads:
-x ‹ -13
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.
</span><span>The last step is to divide both sides of the inequality by -1 like this:
<span>To divide x by 1</span><span>The x just gets copied along in the numerator.</span><span>The answer is x</span><span>-x ÷ -1 = x</span><span>-13 ÷ -1 = 13</span><span>Note! Here's an important point about inequalities:We are now dividing by -1, which is a number less than zero! This changes the form of your inequality. Or, in other words, your ‹ will now become a ›.</span><span>The solution to your inequality is:
x › 13</span></span></span></span></span>
<span>The answer is <span>-13+x</span></span>
