Castle Algebra 1: Two-Step Equations Flashcards

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 $-7 = \frac{c}{-6} + 12$?

c = 114 Signup and view all the answers

What is the solution for the equation $-12 = \frac{6 + 3y}{5}$?

y = -30 Signup and view all the answers

What is the solution for the equation $\frac{u + 12}{-4} = 5$?

u = -32 Signup and view all the answers

What is the solution for the equation $-5x + 5 = 25$?

x = -4 Signup and view all the answers

What is the solution for the equation $3x - 10 = 11$?

x = 7 Signup and view all the answers

What is the solution for the equation $\frac{x}{-2} + 5 = 25$?

x = -40 Signup and view all the answers

What is the solution for the equation $4x - 4 = -20$?

x = -4 Signup and view all the answers

What is the solution for the equation $-9x + 6 = 60$?

x = -6 Signup and view all the answers

What is the solution for the equation $6 + 5n = -4$?

n = -2 Signup and view all the answers

What is the solution for the equation $-7 + 3c = -11$?

c = -\frac{4}{3} Signup and view all the answers

What is the solution for the equation $15 = 4a - 7$?

a = 5.5 Signup and view all the answers

What is the solution for the equation $-63 = 7g - 14$?

g = -7 Signup and view all the answers

What is the solution for the equation $4g - 5 = -6$?

g = -\frac{1}{4} Signup and view all the answers

What is the solution for the equation $18 = -5p + 3$?

p = -3 Signup and view all the answers

What is the solution for the equation $3n + 6 = -42$?

n = -16 Signup and view all the answers

What is the solution for the equation $-7m - 18 = -60$?

m = 6 Signup and view all the answers

What is the solution for the equation $\frac{x}{7} - 4 = 9$?

x = 91 Signup and view all the answers

What is the solution for the equation $\frac{x}{8} + 4 = 3$?

x = -8 Signup and view all the answers

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.

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Description

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.