High School Math : How to solve two-step equations with integers in pre-algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Possible Answers:

Correct answer:

Explanation:

This is a two-step equation.  First simplify the whole numbers by adding 6 to both sides:

Then divide both sides by 2

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

Perform the same operation on both sides of the equation.

Add 3 to both sides.

Divide both sides by 4 and simplify the fraction.

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the following equation for

Possible Answers:

Correct answer:

Explanation:

To solve a two step equation, we want to isolate the variable. This means first "getting rid of" the number which is being added to the variable, in this case . To get rid of the , we first recognize that it is being added, then we do the inverse and subtract  from both sides.

Now, we want to do the inverse of multiplying by , which is dividing by on both sides.

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the following equation for .

Possible Answers:

Correct answer:

Explanation:

We want to first isolate the variable, thus we first try to get rid of the constants being added to the variable, in this case the . To eliminate , we do the inverse of addition, and subtract  from both sides.

Then, we want to do the inverse of dividing by , which is multiplying by . Remember that multiplying two negative terms results in a positive term.

Example Question #5 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the equation for .

Possible Answers:

Correct answer:

Explanation:

Subtract from both sides to get the variables on the same side, and simplify.

Divide both sides by .

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for :

Possible Answers:

Correct answer:

Explanation:

We have two steps to this problem. Remember our end result is to get  isolated on one side of the equation.

First we add  to each side, cancelling out the  on the left side. This brings the equation to .

Remember to get rid of a number we perform the opposite operation. The  is multiplied with the , therefore to cancel it out we will divide by .

 divided by  equals . What we do to one side we must do to the other, therefore we divide  by  also. This becomes .

Example Question #3 : How To Solve Two Step Equations With Integers In Pre Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

The requires the FOIL method (first, outside, inside, last).

Multiplying the first two monomials  equals .

The outside two are  which equals .

The two inside monomials are  which equals .

The last two are  which is .

All together this becomes

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

According to the laws of exponents, if you add you do not add the exponents. Therefore , and the variable term remains . The answer is .

Example Question #9 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

Add  to both sides.

Subtract 13 from both sides.

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

Subtract 14 from each side.

Divide both sides by 6.

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