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Questions and Answers
Find the solution: 4(3x - 6) < 14x - 10
Find the solution: 4(3x - 6) < 14x - 10
x < -7
Which expression is equivalent to (5x - 7)(x + 8)?
Which expression is equivalent to (5x - 7)(x + 8)?
5x² + 33x - 56
What is 3√72 expressed in simplest radical form?
What is 3√72 expressed in simplest radical form?
18√2
What is the solution to the inequality: -10x - 3 ≤ 17?
What is the solution to the inequality: -10x - 3 ≤ 17?
What property justifies the work between Step 1 and Step 2 in the following steps? Step 1: 8x - 1(2x - 3) = 15; Step 2: 8x - 2x + 3 = 15; Step 3: 6x + 3 = 15; Step 4: 6x + 3 - 3 = 15 - 3; Step 5: 6x = 12.
What property justifies the work between Step 1 and Step 2 in the following steps? Step 1: 8x - 1(2x - 3) = 15; Step 2: 8x - 2x + 3 = 15; Step 3: 6x + 3 = 15; Step 4: 6x + 3 - 3 = 15 - 3; Step 5: 6x = 12.
Which expression is equivalent to √96x⁷ in simplest form?
Which expression is equivalent to √96x⁷ in simplest form?
Which expression best represents the mathematical statement: Seven less than one-third the square root of a number?
Which expression best represents the mathematical statement: Seven less than one-third the square root of a number?
What is the value of the expression when a=27 and b=6 for -3 ³√a + b²?
What is the value of the expression when a=27 and b=6 for -3 ³√a + b²?
What is the value of √208x⁵y⁶z³ expressed in simplest radical form?
What is the value of √208x⁵y⁶z³ expressed in simplest radical form?
Find the solution: 12(x + 3) < 4(4x + 2)
Find the solution: 12(x + 3) < 4(4x + 2)
What is the slope and the y-intercept of the line represented by the equation 16x + 4y = 36?
What is the slope and the y-intercept of the line represented by the equation 16x + 4y = 36?
If a liter of soda costs $2.25 and a pineapple costs $1.50, which expression represents the cost of a liters of soda and b pineapples purchased?
If a liter of soda costs $2.25 and a pineapple costs $1.50, which expression represents the cost of a liters of soda and b pineapples purchased?
Which expression is equivalent to (2x³y¹)³?
Which expression is equivalent to (2x³y¹)³?
What is the slope and the y-intercept of the line represented by the equation -2x + 3y = 21?
What is the slope and the y-intercept of the line represented by the equation -2x + 3y = 21?
Which expression is equivalent to (-7x² + 5x - 12) - (-4x² + 8x + 2)?
Which expression is equivalent to (-7x² + 5x - 12) - (-4x² + 8x + 2)?
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Study Notes
Inequalities and Solutions
- Solving inequalities involves isolating the variable; example: 4(3x - 6) < 14x - 10 leads to x < -7.
- Another example is the inequality -10x - 3 ≤ 17, resulting in x ≥ -2.
Algebraic Expressions
- The product of (5x - 7)(x + 8) simplifies to 5x² + 33x - 56.
- An expression like √96x⁷ simplifies to 4x³√6x.
Simplifying Radicals
- The cubic root of 72 reduces to 18√2 while √208x⁵y⁶z³ simplifies to 4x²y³z√13xz.
Mathematical Representation
- The phrase "seven less than one-third the square root of a number" translates to 7 - 1/3√x.
Evaluating Expressions
- Evaluating the expression -3 ³√a + b² when a=27 and b=6 yields a result of 27.
Slope and Intercept
- From the line equation 16x + 4y = 36, the slope is 4/1 and the y-intercept is 9.
- For the equation -2x + 3y = 21, the slope is 2/3 and the y-intercept is 7.
Cost Expressions
- The cost for a liters of soda and b pineapples can be represented by the expression $2.25a + $1.50b.
Properties of Exponents
- The expression (2x³y¹)³ can be simplified to 8x⁹y³.
Expression Simplification
- Simplifying the expression (-7x² + 5x - 12) - (-4x² + 8x + 2) results in -3x² - 3x - 10.
Inequalities
- Solving 12(x + 3) < 4(4x + 2) leads to the solution x > 7.
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