Pre-Algebra : Two-Step Equations

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #11 : Two Step Equations With Decimals

Solve for

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

The goal is to solve for x. To do this we need to get x by itself. There are two terms on the same side of the equation with the variable we want isolate. We must cancel them out.

Add the term not attached to x to both sides:

The red terms cancel out and we add as usual on the right side of the equation.

Now divide both sides by  to completely isolate x:

The red terms cancel to 1. The right side is divided as normal. A short cut for dividing decimals is to relate them to coins or convert them to fractions. On the right side we have $1.50 in the numerator and .75 cents in the denominator. It takes two sets of .75 cents to make a $1.50. So x=2.

If this analogy does not work then convert the decimals to fractions. Three divided by two is 1.5 and 3 divided by 4 is .75. When we divide a fraction by a fraction we multiply the numerator by the reciprocal of the denominator. 

If either of these methods are not easily applicable to the problem, seem like too much work, or are too abstract, then move the decimal of the divisor to make it a whole number. Then move the decimal of the dividend the same number of decimal places. Now divide as usual.

Using this method on the right side of our equation:

 

Example Question #14 : Two Step Equations With Decimals

Find the value of  in the equation.

Possible Answers:

Correct answer:

Explanation:

With a two step equation don't forget when solving the problem do the inverse operation. That means opposite of addition is subtraction and vice versa and opposite of multiplication is division and vice versa. Make sure what ever you do to one side you do to the other as well. Tip: Do addition or subtraction first, then multiplication or division.

             

Check your answer by substituting x back into the equation. Both sides should equal.             

Example Question #111 : Two Step Equations

Solve:  

Possible Answers:

 

Correct answer:

 

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate the unknown variable, first subtract  from both sides.

Divide both sides by .

If dividing by a decimal if difficult, multiply the numerator and denominator by ten to get whole integers.

Now factor the numerator to find a common factor to cancel out.

Example Question #173 : Algebraic Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

To isolate  the unknown variable, first subtract  from both sides.

Example Question #174 : Algebraic Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

To solve for the unknown variable, first subtract  from both sides of the equation.

Divide  on both sides.

If dividing by decimals is difficult, just multiply both decimals by 100 to get integers.

When you multiply by 100 you move the decimal two spaces to the right.

From here factor the numerator and cancel like terms.

Example Question #16 : Two Step Equations With Decimals

Compute:  

Possible Answers:

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract  from both sides of the equation.

Divide  on both sides.

Example Question #112 : Two Step Equations

Solve:  

Possible Answers:

 

Correct answer:

 

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To solve for , combine like-terms by subtracting.

Divide both sides by .

Decimals may be written as fractions. 

 

Dividing by a fraction is the same as multiplying by its reciprocal:

Thus we can replace the decimals with their fraction equivalents:

Canceling out the two that is in the numerator and in the denominator we arrive at our final answer.

Example Question #18 : Two Step Equations With Decimals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Subtract  from both sides of the equation.

Divide by two on both sides.

Example Question #111 : Two Step Equations

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract  on both sides of the equation.

Example Question #21 : Two Step Equations With Decimals

Solve:  

Possible Answers:

Correct answer:

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

First, square the decimal.

Subtract this value from both sides to isolate the unknown variable.

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