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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2271 : Algebra 1

2x + 6y = 44

What is x + 3y + 33 ?

Possible Answers:

The answer cannot be determined.

Correct answer:

Explanation:

The key to solving this question is noticing that we can factor out a 2:

2x + 6y = 44 is the same as 2(x + 3y) = 44.

Therefore, x + 3y = 22.

In this case, x + 3y + 33 is the same as 22 + 33, or 55.

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

Solve for .

5x+15=10y

5y+x=18

Possible Answers:

y=3

x=5

x=15

x=3

Cannot be determined

Correct answer:

x=3

Explanation:

Subtract x from both sides of the second equation.

5y+x=18

5y=18-x

Divide both sides by to get $y=\frac{18-x}{5}$ .

Plug in y to the other equation.

5x+15=10y

$5x+15= 10*\frac{18-x}{5}$

Divide 10 by 5 to eliminate the fraction, yielding 5x+15=2(18-x) .

Distribute the 2 to get 5x+15=36-2x .

Add to each side, and subtract 15 from each side to get 7x=21 .

Divide both sides by 7 to get $\frac{x}{7}=\frac{21}{7}$ , which simplifies to x=3 .

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Example Question #3 : Solving Equations

Solve for :.

18x^3 - 8x = 0

Possible Answers:

$\left \{-\frac{2}{3}, \frac{2}{3} \right \}$

$\left \{-\frac{2}{3}, 0, \frac{2}{3} \right \}$

$\left \{ \frac{3}{2}, 0, -\frac{3}{2} \right\}$

$\left \{ - \frac{3}{2}, \frac{3}{2} \right\}$

Correct answer:

$\left \{-\frac{2}{3}, 0, \frac{2}{3} \right \}$

Explanation:

First factor the expression by pulling out :

18x^3 - 8x = 0

2x(9x^2-4) = 0

Factor the expression in parentheses by recognizing that it is a difference of squares:

2x(3x+2)(3x-2)= 0

Set each term equal to 0 and solve for the x values:

$2x=0 \rightarrow x=0$

$3x+2=0\rightarrow x=-\frac{2}{3}$

$3x-2=0\rightarrow x=\frac{2}{3}$

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Example Question #143 : Equations / Inequalities

Possible Answers:

$\frac{7}{9}$

$\frac{2}{3}$

$\frac{5}{9}$

$\frac{5}{3}$

$\frac{4}{3}$

Correct answer:

$\frac{5}{9}$

Explanation:

1. First, simplify the numerator by finding a common denominator:

$\frac{6}{3}-\frac{4}{12}=\frac{6}{3}-\frac{1}{3}=\frac{5}{3}$

2. Next, simplify the denominator. These fractions can be added together without any additional work:

$\frac{9}{5}+\frac{6}{5}= \frac{15}{5}=3$

3. Then, simplify by multiplying top and bottom by the recriprocal of the denominator:

$\frac{\frac{5}{3}}{3}\cdot\frac{\frac{1}{3}}{\frac{1}{3}}=\frac{\frac{5}{9}}{1}=\frac{5}{9}$

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Example Question #144 : Equations / Inequalities

$A\bigtriangledown B = \frac{-A^2+3(-B)^2}{\frac{2}{A}+\frac{1}B{}}$

$4\bigtriangledown 2=$

Possible Answers:

$-\frac{3}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Here, A=4,B=2 . Plug these values in and simplify.

Start with the numerator first:

-A^2 +3(-B)^2 = -(4)^2 +3(-2)^2= -16 +12=-4

Then do the same in the denominator:

$\frac{2}{A}+\frac{1}{B}= \frac{2}{4}+\frac{1}{2}= \frac{1}{2}+\frac{1}{2}=1$

Finally, combine the two results to find the solution:

$\frac{-4}{1}=-4$

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Example Question #23 : Linear / Rational / Variable Equations

Solve for :

$(x-3)^{2}=36$

Possible Answers:

(6,-6)

(9,-3)

(3,-9)

(9,3)

None of the other answers

Correct answer:

(9,-3)

Explanation:

To solve this equation, you must first eliminate the exponent from the (x-3) by taking the square root of both sides:

$\sqrt{(x-3)^{2}}=\sqrt{36}$

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

x-3=-6

and

x-3=6

to get solutions of (9,-3) .

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Example Question #145 : Equations / Inequalities

Solve for :

ax-b=cd

Possible Answers:

$\frac{cd+b}{a}$

$\frac{b}{cd+a}$

$\frac{a}{cd+b}$

$\frac{cd+a}{b}$

None of the other answers

Correct answer:

$\frac{cd+b}{a}$

Explanation:

To solve for , you must isolate it from the other variables. Start by adding to both sides to give you ax=cd+b . Now, you need only to divide from both sides to completely isolate . This gives you a solution of $x=\frac{cd+b}{a}$ .

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Example Question #4 : Solving Equations And Inequallities

Solve for :

6x-3-4x+5=3(x-1)

Possible Answers:

Correct answer:

Explanation:

Combine like terms on the left side of the equation: 2x+2=3(x-1)

Use the distributive property to simplify the right side of the equation: 2x+2=3x-3

Next, move the 's to one side and the integers to the other side: x=5

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Example Question #146 : Equations / Inequalities

Solve for :

ex+f=g

Possible Answers:

$\frac{g-f}{e}$

None of the other answers

$\frac{e}{g-f}$

$\frac{g+f}{e}$

$\frac{e}{g+f}$

Correct answer:

$\frac{g-f}{e}$

Explanation:

To solve for , you must isolate it so that all of the other variables are on the other side of the equation. To do this, first subtract from both sides to get ex=g-f . Then, divide both sides by to get $x=\frac{g-f}{e}$ .

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Example Question #151 : Equations / Inequalities

The sum of four consecutive integers equal 98. What is the sum of the smallest and the largest number in the set?

Possible Answers:

Correct answer:

Explanation:

Let a variable represent the smallest number in the set. Every consecutive number after the first number will be one unit greater than the other. Then, the four numbers that sum up to 98 are:

(x)+(x+1)+(x+2)+(x+3)=98

where every term in parenthesis represents a number. Add and solve for .

4x+6=98

x=23

The smallest number is , and the largest number is x+3 . Therefore:

x+(x+3)= 23+(23+3)=23+26=49

The correct answer is:

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2271 : Algebra 1

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

Example Question #3 : Solving Equations

Example Question #143 : Equations / Inequalities

Example Question #144 : Equations / Inequalities

Example Question #23 : Linear / Rational / Variable Equations

Example Question #145 : Equations / Inequalities

Example Question #4 : Solving Equations And Inequallities

Example Question #146 : Equations / Inequalities

Example Question #151 : Equations / Inequalities

All Algebra 1 Resources

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