Podcast Beta
Questions and Answers
Which expression below is a ______?
binomial
The value of the expression x² - 22 when x = -6 is ______.
11
The simplified version of 11x² - x - 9 - 5x² - 6x + 4 is ______.
6x² - 7x - 5
The solution to the equation 9(x + 3) = 5(x - 4) + 3 is x = ______.
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The value of 7 - x + 3 when x = -20 is ______.
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In the equation 6(x + 2) + 7 = 5(x + 3) - 7(x - 2), the final answer for x is ______.
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The equation 3(3n + 1) - 5(n - 1) = 2(n + 3) + 2(n + 1) is either an identity or is ______.
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The volume of water in the tank after t minutes is given by the expression 12t + ______.
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Study Notes
Binomial
- A binomial is a polynomial with two terms
- An example of a binomial is x^2 - 2y
Solving Equations
- To rearrange an equation, you can multiply or divide both sides by the same number
- To solve for x in the equation 9(x + 3) = 5(x - 4) + 3, first distribute the 9 and 5
- To combine like terms, add 5x to both sides and subtract 27 from both sides
- The solution to the equation is x = -11
Simplifying Expressions
- To simplify an expression such as 11x^2 - x - 9 - 5x^2 - 6x + 4, you can combine like terms
- Combine the x^2 terms, the x terms, and the constant terms
- The simplified expression is 6x^2 - 7x - 5
Evaluating Expressions
- To evaluate an expression, substitute a given value for the variable
- To evaluate 7 - x + 3 when x = -20, substitute -20 for x
- The result is 7 - (-20) + 3 = 30
Identities and Inconsistent Equations
- An identity is an equation that is true for all values of the variable
- An inconsistent equation is an equation that is never true, no matter what the value of the variable
- The equation 3(3n + 1) - 5(n - 1) = 2(n + 3) + 2(n + 1) is an identity
- To determine if an equation is an identity, simplify both sides of the equation
- If both sides simplify to the same expression, then the equation is an identity
Applications
- The expression 12t + 5 + 7 represents the volume of water in a tank after t minutes
- To find the volume of water in the tank after 11 minutes, substitute t = 11 into the expression
- The answer is 144, meaning that there are 144 gallons of water in the tank after 11 minutes
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Description
This quiz focuses on key concepts in algebra, including binomials, solving equations, simplifying expressions, and evaluating expressions. Test your understanding of these important topics and enhance your algebra skills.
