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

8z - 2z < 51 - 3

6z < 48

z < 48/6

z < 8

Answer: z < 8

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 8 Multiply z and 1 The z just gets copied along. The answer is z z 8*z evaluates to 8z 8*z+3 evaluates to 8z+3 Multiply z and 1 The z just gets copied along. The answer is z z 2*z evaluates to 2z 8z - 2z = 6z The answer is 6z+3 8*z+3-2*z evaluates to 6z+3 So, all-in-all, the left hand side of your inequality can be written as:6z+3 Now, let's work on the right hand side of your inequality, the 51

The right hand side of your inequality can be written as: 51 So 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 = 0 The answer is 6z From 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 1 The z just gets copied along in the numerator. The answer is z 6z : 6 = z 48 : 6 = 8 The solution to your inequality is:

z ‹ 8 t he answer is 48 Multiply z and 2