Algebra 1 : How to solve one-step equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #261 : Linear Equations

What property of equality lets me solve the one-step equation , if I know that ?

Possible Answers:

Transitive Property of Equality

Substitution Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Reflexive Property of Equality

Correct answer:

Substitution Property of Equality

Explanation:

The Substitution Property of Equality tells me that if , then wherever I could write , I may instead substitute  (and vice versa)! This rule underpins most mathematics.

Therefore, if , the Substitution Property of Equality lets me say that ---> .

Example Question #261 : Algebra 1

Solve the following equation:

 

Possible Answers:

Correct answer:

Explanation:

This is a one-step equation where you need to divide both sides by  to get  by itself. 

So,  when you simplify this you get

Example Question #263 : Linear Equations

Solve for :  

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we will need to multiply both sides by .  

Simplify the left and right sides of the equation.

The answer is:  

Example Question #264 : Algebra 1

Solve for 

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Subtract  from both sides of the equation.

Solve.

Example Question #264 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Subtract  from both sides of the equation.

Remember since  is greater than  and is negative, our answer is negative. We will treat the operation as a normal subtraction problem.

Solve.

Example Question #265 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Subtract  from both sides of the equation.

When subtracting a number from a negative number, we will treat the operation as addition and place a negative sign in front of the answer. 

Solve.

Example Question #266 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Add  to both sides of the equation.

Solve.

Example Question #262 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Add  to both sides of the equation.

Remember since  is greater than  and is positive, our answer is positive. We will treat the operation as a normal subtraction problem.

Solve.

Example Question #267 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Add  to both sides of the equation.

Remember since  is greater than  and is negative, our answer is negative. We will treat the operation as a normal subtraction problem.

Solve.

Example Question #268 : Linear Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve for , we need to isolate the variable on the left side of the equation.  We will do this by performing the reverse operations that were done on the variable to both sides of the equation.

 

Divide both sides of the eqaution by .

Solve.

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