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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #141 : Equations / Inequalities

Simplify the result of the following steps, to be completed in order:

1. Add to

2. Multiply the sum by

3. Add to the product

4. Subtract from the sum

Possible Answers:

28x -13y

28x + 11y

28x + 12y

28x + 13y

29x + 13y

Correct answer:

28x + 13y

Explanation:

Step 1: 7x + 3y

Step 2: 4 * (7x + 3y) = 28x + 12y

Step 3: 28x + 12y + x = 29x + 12y

Step 4: 29x + 12y – (x – y) = 29x + 12y – x + y = 28x + 13y

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Example Question #142 : Equations / Inequalities

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 #4 : Solving Equations

Solve for :.

18x^3 - 8x = 0

Possible Answers:

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

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

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

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

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:

$\frac{5}{3}$

$\frac{2}{3}$

$\frac{7}{9}$

$\frac{5}{9}$

$\frac{4}{3}$

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:

$-\frac{1}{2}$

$-\frac{3}{2}$

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 #1 : Quadratic Roots

Solve for :

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

Possible Answers:

(6,-6)

(3,-9)

(9,3)

None of the other answers

(9,-3)

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:

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

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

None of the other answers

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

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

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 #3 : 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:

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

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

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

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

None of the other answers

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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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #141 : Equations / Inequalities

Example Question #142 : Equations / Inequalities

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

Example Question #4 : Solving Equations

Example Question #143 : Equations / Inequalities

Example Question #144 : Equations / Inequalities

Example Question #1 : Quadratic Roots

Example Question #145 : Equations / Inequalities

Example Question #3 : Solving Equations And Inequallities

Example Question #146 : Equations / Inequalities

All Algebra 1 Resources

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