# solving any linear equation

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Discuss the following:

I. Given a 1-variable linear equation 10z-4=86. Explain the techniques, and show the steps used for solving this equation. Check if the solution is correct.

II. Using the same 1-variable linear equation in I above, change the linear equation to a linear inequality (Use either < or >). Explain the techniques, and show the steps used for manipulating the linear inequality. Check if the solution is correct.

III. Interpret the solution to the linear equation and inequality, and explain the differences in results. Explain how the obtained value is a solution for the inequality.

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I. Given a 1-variable linear equation 10z-4=86. Explain the techniques, and show the steps used for solving this equation. Check if the solution is correct.

In solving any linear equation the goal is to find what value makes the statement true. In other words what value for z can be substituted so that 10z - 4 = 86. To find this value we must isolate the variable in the equation so that only the variable (z) remains on one side of the equation.

1.) To start the process we must make sure that both sides of the equation are simplified as much as possible. If there are any like terms to be combined that should be done first. In this example there is nothing to be done so we can proceed to the next step.

2.) Next we must see if there is any type of constant that can be added or subtracted from the left side of the equation. Now it should be obvious to see that 4 is being subtracted from the term ...

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