Questions and Answers
What is the solution for the equation $5x + 3 = 23$?
x = 4
What is the solution for the equation $6 - 5c = -29$?
c = 7
What is the solution for the equation $0.4x - 3 = -1$?
x = 5
What is the solution for the equation $-7 = \frac{c}{-6} + 12$?
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What is the solution for the equation $-12 = \frac{6 + 3y}{5}$?
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What is the solution for the equation $\frac{u + 12}{-4} = 5$?
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What is the solution for the equation $-5x + 5 = 25$?
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What is the solution for the equation $3x - 10 = 11$?
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What is the solution for the equation $\frac{x}{-2} + 5 = 25$?
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What is the solution for the equation $4x - 4 = -20$?
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What is the solution for the equation $-9x + 6 = 60$?
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What is the solution for the equation $6 + 5n = -4$?
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What is the solution for the equation $-7 + 3c = -11$?
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What is the solution for the equation $15 = 4a - 7$?
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What is the solution for the equation $-63 = 7g - 14$?
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What is the solution for the equation $4g - 5 = -6$?
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What is the solution for the equation $18 = -5p + 3$?
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What is the solution for the equation $3n + 6 = -42$?
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What is the solution for the equation $-7m - 18 = -60$?
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What is the solution for the equation $\frac{x}{7} - 4 = 9$?
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What is the solution for the equation $\frac{x}{8} + 4 = 3$?
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Study Notes
Two-Step Equations Overview
- Two-step equations require two operations to isolate the variable.
- Common operations include addition, subtraction, multiplication, and division.
Key Example Equations and Solutions
-
5× + 3 = 23
- Solution: x = 4
-
6 - 5c = -29
- Solution: c = 7
-
0.4× - 3 = -1
- Solution: x = 5
-
-7 = c / -6 + 12
- Solution: c = 114
-
-12 = 6 + 3y / 5
- Solution: y = -30
Variable Isolation Techniques
- To solve (u + 12) / -4 = 5, rearranging yields u = -32.
- For -5x + 5 = 25, the result is x = -4.
- In the equation 3x - 10 = 11, it simplifies to x = 7.
Handling Negative Values
- x / -2 + 5 = 25 simplifies to x = -40.
- 4x - 4 = -20 produces x = -4.
- -9x + 6 = 60 results in x = -6.
Working with Fractions
- Example: 6 + 5n = -4 leads to n = -2.
- Solving -7 + 3c = -11 gives c = -4/3.
Real-World Application
- Equations can represent various situations like finance, physics, etc.
- Example of a practical scenario: Solving for a variable to determine an unknown cost or value.
Advanced Examples
- 15 = 4a - 7 results in a = 5.5.
- -63 = 7g - 14 gives g = -7.
- The equation 4g - 5 = -6 simplifies to g = -1/4.
Additional Problem Solving
- 18 = -5p + 3 produces p = -3.
- 3n + 6 = -42 leads to n = -16.
- The equation -7m - 18 = -60 results in m = 6.
More Variable Examples
- Solving x / 7 - 4 = 9 gives x = 91.
- For x / 8 + 4 = 3, the solution is x = -8.
Studying That Suits You
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Test your knowledge of two-step equations with these flashcards from Castle Algebra 1. Each card presents an equation along with its solution, helping you practice key algebra concepts effectively. Perfect for reinforcing your understanding of solving equations in Algebra 1.