Questions and Answers
Evaluate the expression: 11 + 8 x 3^ - 8
75
Evaluate the expression: 2/3 ((5 + 2)^ - 13)
24
Evaluate the expression: 5k^ - 7k when k=3
24
Write an equation or an inequality for: 3 times the sum of 7 and a number y
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Write an equation or an inequality for: 4 less than the quantity 6 times a number n
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Write an equation or an inequality for: The difference of 22 and the square of a number m
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Check whether the given number is a solution of the equation 7x-11=17 when x=4.
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Check whether the given number is a solution of the inequality 9y + 3 < 13 when y=2.
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Check whether the given number is a solution of the inequality 5z - 9 >= 7z - 11 when z=-2.
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Solve: 5 + (-13)
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Solve: -17 + (-21)
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Solve: 15 - (-12)
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Calculate: -7(-11)
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Calculate: -1/2(15)(-8)
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Calculate: 72/-6
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Find the square root of 169.
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Find the negative square root of 9.
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Find the positive and negative square roots of 256.
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Find the positive and negative square roots of 0.04.
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Solve, if possible: x + 7 = 19.
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Solve, if possible: 23 - y = 14.
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Solve, if possible: 7p - 11 = 10.
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Solve, if possible: q/4 + 8 = 13.
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Solve, if possible: 15j + 7 j = 11.
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Solve, if possible: 14m + 7 - 8m = -17.
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Solve, if possible: -3.1t + 4.3 = -1.9t + 3.7.
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Solve, if possible: 3(4k - 2) = 16k -32.
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Solve, if possible: 1/3(9g - 6) = 3/5(5g + 15).
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A student can read 4 pages in 5 minutes. How many pages can the student read in 60 minutes?
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What percent of 38 is 15.2?
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What number is 35% of 150?
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At your school, 74% of students bought their lunch at the cafeteria. How many students bought their lunch?
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Solve ax + by = c for a.
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Solve ax - y/b =c for y.
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Solve and graph: x - 13 < -8.
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Study Notes
Evaluating Expressions
- The result of evaluating 11 + 8 x 3^ - 8 is 75 after applying order of operations.
- Evaluating 2/3 ((5 + 2)^ - 13) results in 24.
- For 5k - 7k when k=3, the answer is 24.
Writing Equations and Inequalities
- The expression for "3 times the sum of 7 and a number y" is 3(7+y).
- "4 less than the quantity 6 times a number n" translates to 6n - 4.
- The expression for "the difference of 22 and the square of a number m" is 22 - m^2.
Checking Solutions of Equations and Inequalities
- For 7x - 11 = 17 with x=4, it verifies to yes (17=17).
- Check if 9y + 3 < 13 with y=2; it does not hold true (21 < 13 is false).
- For 5z - 9 ≥ 7z - 11 with z=-2, it does not satisfy the inequality (1 ≥ 24 is false).
Basic Operations and Results
- The result of 5 + (-13) is -8.
- Evaluating -17 + (-21) gives -38.
- For 15 - (-12), the answer is 27.
Multiplication and Division
- -7 multiplied by -11 results in 77.
- -1/2 × 15 × -8 equals 60.
- Dividing 72 by -6 yields -12.
Square Roots
- The square root of 169 is 13.
- The negative square root of 9 is -3.
- Both positive and negative square roots of 256 are 16 and -16.
Solving Linear Equations
- Solve x + 7 = 19 to find x = 12.
- From 23 - y = 14, solving yields y = 9.
- For 7p - 11 = 10, the solution is p = 3.
- From q/4 + 8 = 13, derive q = 20.
- The equation 15j + 7j = 11 simplifies to j = 1/2.
- For 14m + 7 - 8m = -17, the solution is m = -4.
More Complex Equations
- The equation -3.1t + 4.3 = -1.9t + 3.7 results in t = 1/2.
- Solve 3(4k - 2) = 16k - 32, yielding k = 13/2.
- The equation 1/3(9g - 6) = 3/5(5g + 15) results in no possible solution.
Application Problems
- A student reading 4 pages in 5 minutes can read 75 pages in 60 minutes.
- To find what percent of 38 is 15.2, it computes to 40%.
- Calculating 35% of 150 gives 52.5.
- At a school with 1250 students, 925 students bought lunch at the cafeteria.
Solving for Variables
- Rearranging ax + by = c for a results in a = (-by + c)/x.
- To solve for y in ax - y/b = c, we find y = abx - bc.
Solving and Graphing Inequalities
- For the inequality x - 13 < -8, it simplifies to x < 5.
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