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Questions and Answers
What is the value of $x$ in the equation $3x + 6 = 21$?
Which of the following expressions simplifies to $4(2x + 3) - 2(3x - 1)$?
If $a = 2$ and $b = 3$, what is the value of the expression $3a^2 + 2b$?
Which of the following represents the area of a rectangle with length $l$ and width $w$?
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What is the result of solving the inequality $2x - 5 < 1$?
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Study Notes
Solving Linear Equations
- To find the value of ( x ) in the equation ( 3x + 6 = 21 ), isolate ( x ) by performing the following steps:
- Subtract 6 from both sides: ( 3x = 15 )
- Divide both sides by 3: ( x = 5 )
Simplifying Expressions
- The expression ( 4(2x + 3) - 2(3x - 1) ) can be simplified by distributing:
- Distribute ( 4 ) to ( (2x + 3) ): ( 8x + 12 )
- Distribute ( -2 ) to ( (3x - 1) ): ( -6x + 2 )
- Combine like terms: ( 8x - 6x + 12 + 2 = 2x + 14 )
Evaluating Algebraic Expressions
- For ( a = 2 ) and ( b = 3 ), substitute values into the expression ( 3a^2 + 2b ):
- Calculate ( a^2 ): ( 2^2 = 4 )
- Multiply by 3: ( 3 \cdot 4 = 12 )
- Calculate ( 2b ): ( 2 \cdot 3 = 6 )
- Add both results: ( 12 + 6 = 18 )
Geometry Basics
- The area ( A ) of a rectangle is determined by the formula:
- ( A = l \times w ), where ( l ) is the length and ( w ) is the width.
Solving Inequalities
- To solve the inequality ( 2x - 5 < 1 ):
- Add 5 to both sides: ( 2x < 6 )
- Divide both sides by 2: ( x < 3 )
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Description
Test your skills with this Mathematics review for the 8th grade first quarter! This quiz covers equations, expressions, geometric formulas, and inequalities. Answer questions including solving for x, simplifying expressions, and understanding areas of rectangles.
