Solve this inequality 8z+3-2z< 51

First, let's work on the left hand side of your inequality, the 8z+3-2z
This means, for instance, to see if it can be simplified at all.
Multiply z and 8Multiply z and 1The z just gets copied along.The answer is zz8*z evaluates to 8z8*z+3 evaluates to 8z+3Multiply z and 1The z just gets copied along.The answer is zz2*z evaluates to 2z8z - 2z = 6zThe answer is 6z+38*z+3-2*z evaluates to 6z+3So, all-in-all, the left hand side of your inequality can be written as:6z+3Now, let's work on the right hand side of your inequality, the 51
The right hand side of your inequality can be written as: 51So with these (any) simplifications, the inequality we'll set out to solve is:
6z+3 ‹ 51
Move the 3 to the right hand side by subtracting 3 from both sides, like this:
From the left hand side:
3 - 3 = 0The answer is 6zFrom the right hand side:
51 - 3 = 48
Now, the inequality reads:
6z ‹ 48 
To isolate the z, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the z on the left side of the inequality.
The last step is to divide both sides of the inequality by 6 like this:
To divide z by 1The z just gets copied along in the numerator.The answer is z6z ÷ 6 = z48 ÷ 6 = 8The solution to your inequality is:
z ‹ 8 the answer is 48 Multiply z and 2

8z - 2z < 51 - 3 
6z < 48 
z < 48/6 
z < 8 
z < 8