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Questions and Answers
What is the value of $x$ in the equation $3x + 6 = 21$?
What is the value of $x$ in the equation $3x + 6 = 21$?
- 7
- 5 (correct)
- 15
- 3 (correct)
Which of the following expressions simplifies to $4(2x + 3) - 2(3x - 1)$?
Which of the following expressions simplifies to $4(2x + 3) - 2(3x - 1)$?
- $2x + 10$
- $2x + 14$
- $10 - x$ (correct)
- $10 + x$
If $a = 2$ and $b = 3$, what is the value of the expression $3a^2 + 2b$?
If $a = 2$ and $b = 3$, what is the value of the expression $3a^2 + 2b$?
- 12 (correct)
- 6
- 18
- 10
Which of the following represents the area of a rectangle with length $l$ and width $w$?
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 $2x - 5 < 1$?
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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