First, let's work on the left hand side of your inequality, the -134
This means, for instance, to see if it can be simplified at all.
Because of the minus sign
134 becomes - 134
The answer is -134
So, all-in-all, the left hand side of your inequality can be written as: -134 Now, let's work on the right hand side of your inequality, the 8x-5
Multiply x and 8
Multiply x and 1
The x just gets copied along.
The answer is x
x
8x evaluates to 8x
8x-5 evaluates to 8x-5
The right hand side of your inequality can be written as: 8x-5
So with these (any) simplifications, the inequality we'll set out to solve is:
-134 ‹ 8x-5
Move the -134 to the right hand side by adding 134 to both sides, like this:
To the left hand side:
-134 + 134 = 0
The answer is 0
To the right hand side:
-5 + 134 = 129
The answer is 129+8x
Now, the inequality reads:
0 ‹ 129+8x
Move the 8x to the left hand side by subtracting 8x from both sides, like this:
From the left hand side:
The answer is -8x
From the right hand side:
8x - 8x = 0
The answer is 129
Now, the inequality reads:
-8x ‹ 129
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.
The last step is to divide both sides of the inequality by -8 like this:
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
-8x ÷ -8 = x
129 ÷ -8 =
Note! Here's an important point about inequalities:We
are now dividing by -8, which is a number less than zero! This changes
the form of your inequality. Or, in other words, your ‹ will now become a ›.The solution to your inequality is:
x ›
