Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #162 : How To Solve Two Step Equations

Solve the equation for :

Possible Answers:

Correct answer:

Explanation:

Start by adding  on both sides of the equation to yield:

In order to get  by itself, we need to divide both sides of the equation by

.

This gives us

Example Question #170 : How To Solve Two Step Equations

Possible Answers:

Correct answer:

Explanation:

First, isolate variables and constants on either side of the equal sign. In this case, subtract  from both sides. This gives us:

.

Now divide both sides by  to give us:

.

Example Question #171 : How To Solve Two Step Equations

Solve for 

Possible Answers:

Correct answer:

Explanation:

 State the equation.

 Subtract  from both sides. (Substitution property of equality)

 Divide both sides by . (Division property of equality)

Example Question #172 : How To Solve Two Step Equations

Solve the equation: 

Possible Answers:

Correct answer:

Explanation:

 State the equation.

 Square both sides.

 Divide both sides by .

Example Question #173 : How To Solve Two Step Equations

Solve the equation: 

Possible Answers:

Correct answer:

Explanation:

 State the equation.

 Cube root both sides.

 Subtract  from both sides.

Example Question #174 : How To Solve Two Step Equations

What order of operations would result in solving the equation for ?

Possible Answers:

Taking the root, then division, then addition

Cubing, then division, then addition

Division, then taking the root, then subtraction

Multiplication, then taking the root, then subtraction

Taking the root, then subtraction, then division

Correct answer:

Taking the root, then subtraction, then division

Explanation:

 Take the root.

 Subtract  from both sides.

 Divide both sides by  and simplify.

Example Question #171 : How To Solve Two Step Equations

What order of operations would be used to solve the equation ?

Possible Answers:

Multiplication, then addition

Addition, then multiplication

Division, then addition

Multiplication, then subtraction

Division, then subtraction

Correct answer:

Multiplication, then addition

Explanation:

 State the problem (not an actual step, but useful!)

 Multiply both sides by .

 Add  to both sides.

Example Question #176 : How To Solve Two Step Equations

What is the least number of operations (not counting simplification of fractions) needed to solve for ?

Possible Answers:

Correct answer:

Explanation:

 State the problem (not a required step, but it helps!)

 Take the fifth root of both sides. (Step 1)

 Subtract  from both sides. (Step 2)

Example Question #177 : How To Solve Two Step Equations

Solve:  

Possible Answers:

Correct answer:

Explanation:

To solve, multiply both sides by .

Simplify the left side by cancelling the  and multiplying the right side.

Divide both sides by  to isolate .

The answer is:  

Example Question #178 : How To Solve Two Step Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides.

 Divide  on both sides.

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