Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #152 : Equations / Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

The question asks for the value of .

To isolate , use the distributive properties to remove the parentheses then combine like terms.

Finally isolate  by balancing the equation.

Example Question #153 : Equations / Inequalities

Find the solution to this equation: 

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

To find the solution to this equation you must completely isolate x. 

Start by dealing with the parenthesis first. Distribute the 25:

Combine the x terms and move the constant over:

Finally divide the constant away from x to solve:

Example Question #3 : Solving Equations And Inequallities

Solve for x: 

Possible Answers:

Correct answer:

Explanation:

Simplify the parenthesis:

Combine the terms with x's:

Combine constants:

Example Question #152 : Equations / Inequalities

Solve for x:   

Possible Answers:

None of these

Correct answer:

Explanation:

Simplify the right side:

Isolate x:

Example Question #31 : Linear / Rational / Variable Equations

Solve for 

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

Possible Answers:

Correct answer:

Explanation:

First. combine like terms to get

.

Then, add  and subtract from both sides to separate the terms.

This gives you .

Finally, divide both sides by  to get a solution of .

Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

Possible Answers:

None of the other answers

Correct answer:

Explanation:

First, you must multiply the left side of the equation using the distributive property.

This gives you .

Next, subtract  from both sides to get .

Then, divide both sides by  to get .

Example Question #32 : Linear / Rational / Variable Equations

  

If , find the value of .

 

Possible Answers:

Correct answer:

Explanation:

The simplest way to solve this is to test the answer choices provided by plugging them in the equation.  Start with the number in the middle, which in this case is 6. Replace every "B" in the equation with "6", and solve.

 

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

Before you can add the two numerators from the fractions, the fractions must have a common denominator. The common denominator will be the Lowest Common Denominator (LCD). When you are dealing with variables, you get this by multiplying the two denominators together:

To follow through with this LCD, you must multiply each fraction by the other fraction's denominator so that they end up with common denominators. The first fraction needs to be multiplied by  and the second fraction needs to be multiplied by . Note that both of these are equivalent to ONE, so the value of the fraction does not change:

Now that the two fractions have common denominators, you can add the two numerators:

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

Before you can subtract the two numerators from the fractions, the fractions must have a common denominator. The common denominator will be the Lowest Common Denominator (LCD). When you are dealing with variables, you get this by multiplying the two denominators together:

To follow through with this LCD, you must multiply each fraction by the other fraction's denominator so that they end up with common denominators. The first fraction needs to be multiplied by  and the second fraction needs to be multiplied by . Note that both of these are equivalent to ONE, so the value of the fraction does not change:

Now that the two fractions have common denominators, you can subtract the two numerators. You can also distribute the denominator so you can simplify later:

Finally you can divide out each term in the numerator and denominator by 2 to fully simplify the answer:

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