Questions and Answers
What is the value of 'a' in the equation $2a - 7 = -15$?
-4
What is the value of 'x' in the equation $3 = -6x + 15$?
2
What is the value of 'c' in the equation $\frac{c}{4} + 10 = 22$?
48
What is the value of 'y' in the equation $1.5y + 3.4 = 7.9$?
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What is the value of 'y' in the equation $\frac{2}{3}y - 9 = 5$?
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What is the value of 'x' in the equation $8 = 9x - 7$?
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What is the value of 'm' in the equation $8m - 3m = 4$?
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What is the value of 'y' in the equation $6 - 2y - y = 12$?
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What are the values of 'q' in the equation $\frac{2}{3}q + 5 = \frac{3}{4}$?
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What is the value of 'c' in the equation $-2(5 + 6c) + 16 = -90$?
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What was the original price if a pair of jeans is on sale for 15% off and the sale price is $29.74?
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How many tens and twenties does the bank teller have if his total is $1,167 and he has $147 in other bills?
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What is the value of 'x' in the equation $7x = 33 - 4x$?
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What is the value of 'a' in the equation $2a - 24 - 3a = 5a$?
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What is the value of 'b' in the equation $8(b + 3) = 2b - 4$?
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What is the value of 'x' in the equation $2x - (9 - 3x) = 8x - 11$?
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What is the solution for 'a' in the inequality $2a - 3 > 11$?
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What does the inequality $9y + 13$ tell us about 'y'?
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What does the inequality $-6c + 12$ tell us about 'c'?
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What is the value of 'x' in the inequality $\frac{8}{9}x + 5 < -3$?
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What is the value of 'x' in the inequality $-17 > \frac{x}{3} - 19$?
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Study Notes
Equations and Solutions
- Solve (2a - 7 = -15) results in (a = -4).
- Solve (3 = -6x + 15) results in (x = 2).
- Solve (\frac{c}{4} + 10 = 22) results in (c = 48).
- Solve (1.5y + 3.4 = 7.9) results in (y = 3).
- Solve (\frac{2}{3}y - 9 = 5) results in (y = 21).
- Solve (8 = 9x - 7) results in (x = \frac{5}{3}).
Additional Equations
- Solve (8m - 3m = 4) results in (m = \frac{4}{5}).
- Solve (6 - 2y - y = 12) results in (y = -2).
- Solve (\frac{2}{3}q + 5 = \frac{3}{4}) results in (q = -6 \text{ and } \frac{3}{8}).
- Solve (-2(5+6c) + 16 = -90) results in (c = 8).
Real-Life Applications
- Calculate the original price of jeans after a 15% discount leading to a sale price of $29.74; original price is $34.99.
- A bank teller has an equal number of $10 and $20 bills amounting to $1,167; with $147 in other bills, he has 34 tens and 34 twenties.
Inequalities
- Solve (7x = 33 - 4x) leading to (x = 3).
- Solve (2a - 24 - 3a = 5a) leading to (a = -4).
- Solve (8(b + 3) = 2b - 4) leading to (b = -7).
- Solve (2x - (9 - 3x) = 8x - 11) leading to (x = \frac{2}{3}).
Compound and Relative Inequalities
- From (2a - 3 > 11), the solution for (a) is (a > 7).
- Solve (9y + 13 \leq -14) yielding (y \leq -3).
- From (-6c + 12 \geq 8), solving gives (c \leq \frac{2}{3}).
- Solve (\frac{8}{9}x + 5 < -3) leading to (x < -\frac{3}{5}).
Expression Interpretation
- Solve (-17 > \frac{x}{3} - 19), providing an inequality leading to JavaScript variables or constraints on (x).
Studying That Suits You
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Test your knowledge of pre-algebra concepts with these flashcards. Solve for variables in various equations and strengthen your skills in basic algebra. Each flashcard presents an equation along with the solution for effective learning.
