Abeka Algebra 1 Test 2 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following is a solution to $x + 2 = 11$?

9 (correct)

Which of the following is true about a contradiction?

It has one solution

It is always true

It has infinitely many solutions

It has no solutions (correct)

Which of the following states that if any quantity is added to (or subtracted from) both sides of an equation, the equation remains true?

Multiplication property of equality

Subtraction property of equality

Division property of equality

Addition property of equality (correct)

Which of the following values would be multiplied to $\frac{3}{2}x - \frac{5}{9}x + 2$ to clear the equation of fractions?

18 Signup and view all the answers

Which of the following values would be multiplied to $0.56x - 0.98x + 0.734 = 0.43x$ to clear the equations of decimals?

1,000 Signup and view all the answers

What is the outcome of the equation $3x - 1 = 3x + 1$?

Contradiction Signup and view all the answers

Solve the equation $4x - 11 = 7$.

Conditional Signup and view all the answers

What type of equation is $2 - 8x = 2 - 8x$?

Identity Signup and view all the answers

What is the solution for $x - 1 = -x + 4$?

Conditional Signup and view all the answers

What is the solution for $2 \frac{1}{2} x = 10$?

x = 4 Signup and view all the answers

What is the solution for $2n + 5 = n - 7$?

n = -12 Signup and view all the answers

What is the solution for $3x - (2x + 7) = 15$?

x = 22 Signup and view all the answers

What is the solution for $\frac{3}{8}x + 7 = 13$?

x = 16 Signup and view all the answers

What is the solution for $0.7x - 1.2 = 0.3x$?

x = 3 Signup and view all the answers

What is the solution for $5(3x + 2) = 7x - 2$?

x = -\frac{3}{2} Signup and view all the answers

What is the solution for $|2x + 1| = 3$?

x = 1, -2 Signup and view all the answers

What is the solution for $3|4x + 1| + 10 = 7$?

No solution Signup and view all the answers

What is the solution for $5|x - 1| - 2 = 23$?

x = -4, 6 Signup and view all the answers

In a class of 42 students, the number of boys is 12 fewer than twice the number. If the sum of the two numbers is 84, what is the equation?

x + 2x - 12 = 42 Signup and view all the answers

One of the numbers is 40% more than another number. If the sum of both numbers is 84, what is the equation?

x + 1.4x = 84 Signup and view all the answers

Mrs. Hill is 4 years older than twice her son's age. If the sum of their ages is 50, what is the equation?

x + 2x + 4 = 50 Signup and view all the answers

For the formula $V = I R$, what is V?

V = IR Signup and view all the answers

For the formula $V = lwh$, what is h?

h = \frac{V}{lw} Signup and view all the answers

For the equation $2x + 5y = 7$, what is y?

y = \frac{7 - 2x}{5} Signup and view all the answers

For the formula $V = \frac{1}{3} S^2 h$, what is h?

h = \frac{3V}{S^2} Signup and view all the answers

Kathryn bought an aquarium that should be filled with 9 cubic feet of water. If the aquarium is 2 feet wide and 3 feet long, how high should the water fill the aquarium?

1.5 ft. Signup and view all the answers

Mr. Morgan invested $20,000 in an account earning 4.5% interest. How many years would it take for him to earn $5,400 in simple interest?

6 yr. Signup and view all the answers

Mary and her father traveled 420 miles, with three times the distance in the afternoon as in the morning. How far did they travel in the morning?

105 mi. Signup and view all the answers

What is a conditional equation?

An equation that has a finite number of solutions. Signup and view all the answers

What is a contradiction?

An equation that is never true for any value of the variables. Signup and view all the answers

What is an identity?

An equation that is true for every value of the variable. Signup and view all the answers

What is an absolute value equation?

Multiply the equation by 1 and then by -1 and solve for each. Signup and view all the answers

Study Notes

Algebraic Solutions

A solution to the equation (x + 2 = 11) is (x = 9).
A contradiction in equations has no solutions.
The Addition Property of Equality states that adding or subtracting the same quantity from both sides of an equation maintains equality.

Equation Manipulation

To clear fractions in ( \frac{3}{2}x + \frac{-5}{9}x + 2), multiply by (18).
To eliminate decimals in the equation (0.56x - 0.98x + 0.734 = 0.43x), multiply by (1,000).

Types of Equations

The equation (3x - 1 = 3x + 1) is a contradiction, meaning no values of (x) satisfy it.
(4x - 11 = 7) and (x - 1 = -x + 4) are conditional equations, indicating they result in a unique solution.
The identity (2 - 8x = 2 - 8x) holds true for all (x).

Solving for Variables

The equation (2 \frac{1}{2} x = 10) yields (x = 4).
In the equation (2n + 5 = n - 7), the solution is (n = -12).
The equation (3x - (2x + 7) = 15) simplifies to (x = 22).
From ( \frac{3}{8}x + 7 = 13), the solution for (x) is (16).
Solving (0.7x - 1.2 = 0.3x) results in (x = 3).

Variable Isolations

The equation (5(3x + 2) = 7x - 2) simplifies to find (x = -\frac{3}{2}).
For the absolute value equation ( |2x + 1| = 3), solutions are (x = 1) and (x = -2).
The equation (3|4x + 1| + 10 = 7) results in no solutions.
From the equation (5|x - 1| - 2 = 23), solutions found are (x = -4) and (x = 6).

Word Problems and Applications

In a class of 42, where the number of boys is 12 fewer than twice the number of girls, the equation (x + 2x - 12 = 42) expresses the relationships.
For the scenario where one number is 40% more than another and their sum is 84, the equation (x + 1.4x = 84) is used.
Mrs. Hill's age relationship with her son can be modeled with (x + 2x + 4 = 50).

Formulas

Ohm's Law is given by (V = IR), relating voltage (V), current (I), and resistance (R).
Volume (V) of a rectangular prism is calculated using (V = lwh) where (l) is length, (w) is width, and (h) is height.
The formula for solving for y in the linear equation (2x + 5y = 7) is (y = \frac{7 - 2x}{5}).
The height (h) in conical structures can be derived from (h = \frac{3V}{S^2}), where (S) is the base area.

Geometric Applications

To fill an aquarium measuring (2) feet wide and (3) feet long with a volume of (9) cubic feet, the height of the water must be (1.5) feet.

Interest Calculations

Mr. Morgan's investment to earn (5400) dollars at (4.5%) interest will take (6) years.

Travel and Rate Problems

If Mary and her father traveled (420) miles with (3) times the distance in the afternoon compared to the morning, the morning distance equals (105) miles.

Equation Types

Conditional equations yield a finite number of solutions.
Contradictions imply no possible solutions.
Identities are valid for every possible value of the variable.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge of Algebra 1 concepts with these flashcards from Abeka's Test 2. This quiz covers essential algebraic principles including solutions to equations and properties of equality. Perfect for reviewing and reinforcing your understanding of fundamental algebra topics.