Questions and Answers
Which of the following is the correct formula to convert °C to °F?
F = (C * 1.8) + 32
If Antonio can drive home after working less than 7 hours or after working more than 9 hours, how can this be written as a single compound inequality?
h < 7 or h > 9
Which number line represents the solutions to the equation –2|x| = –6?
Number line A
Which explains whether Johan's solutions for the equation –2|8 – x| – 6 = –12 are correct?
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What is the result of converting 50°C to °F?
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Which situation could be represented by the graph?
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What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
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Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h?
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The tables represent the functions f(x) and g(x). Which input value produces the same output value for the two functions?
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Deepak wrote out the steps to his solution of the equation – 3x – 5 + 4x = –. Which step has an incorrect instruction?
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Which expression represents the conversion of 20°F to °C?
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What is the compound inequality that represents Antonio driving home after working less than 7 hours or after working more than 9 hours?
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Which number line represents the solutions to the equation |2x| = -6?
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The equation -3|x - 4| - 5 = -2 has how many possible solutions?
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Which situation could be represented by the graph?
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What is the equivalent compound inequality for the statement 'z is greater than -3 or less than or equal to 5'?
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What is the solution to the equation –9x + 1 = –x + 17?
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What is the value of y in the equation y + 3 = –y + 9?
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What is the solution to the inequality 2(4x – 3) ≥ –3(3x) + 5x?
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What is the value of n in the equation n = 0?
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What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
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In the equation p = 0.7(rh + b), what is an equivalent equation solved for h?
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In the functions f(x) and g(x), which input value produces the same output value for the two functions?
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Which step in Deepak's solution to the equation –3x – 5 + 4x = – is incorrect?
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Lily begins solving the equation: 4(x – 1) – x = 3(x + 5) – 11. How can her partial solution be interpreted?
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'Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b.' Which of the following is another correct form of the given equation?
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Study Notes
Temperature Conversion
- The correct formula to convert °C to °F is °F = (°C × 9/5) + 32.
- 50°C is equivalent to 122°F.
Inequalities
- Antonio can drive home after working less than 7 hours or after working more than 9 hours, which can be represented as a single compound inequality: x < 7 or x > 9.
- The equivalent compound inequality for the statement 'z is greater than -3 or less than or equal to 5' is z > -3 or z ≤ 5.
Absolute Value Equations
- The equation –2|x| = –6 has no solutions.
- The equation |2x| = –6 has no solutions.
- The equation –3|x - 4| - 5 = –2 has two possible solutions.
Functions
- Anastasia's equation p = 0.7(rh + b) can be solved for h as h = (p - 0.7b)/0.7r.
- The input value that produces the same output value for the functions f(x) and g(x) is x = 2.
Solving Equations
- A correct first step in solving the inequality –4(3 – 5x) ≥ –6x + 9 is to distribute the –4 to the terms inside the parentheses.
- The solution to the equation –9x + 1 = –x + 17 is x = 2.
- The solution to the equation y + 3 = –y + 9 is y = 3.
- The solution to the inequality 2(4x – 3) ≥ –3(3x) + 5x is x ≥ 3/2.
Miscellaneous
- Deepak's solution to the equation –3x – 5 + 4x = – has an incorrect instruction in the step where he adds 5 to both sides.
- Lily's partial solution to the equation 4(x – 1) – x = 3(x + 5) – 11 can be interpreted as simplifying the left side to 3x – 4 = 3x + 10, which is incorrect.
- Anastasia's equation p = 0.7(rh + b) can be rewritten as p/0.7 = rh + b, which is another correct form of the given equation.
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