Algebra Two-Step Equations Flashcards

Two-Step Equations Overview

• Two-step equations typically involve isolating the variable through two operations: addition/subtraction followed by multiplication/division.

Key Examples of Equations and Solutions

• Equation: 3x - 7 = 8
• Solution:* x = 5
• Equation: -3x - 7 = 8
• Solution:* x = -5
• Equation: 6x + 2 = -1
• Solution:* x = -1/2
• Equation: -4x + 6 = 34
• Solution:* x = -7
• Equation: -4x - 6 = 34
• Solution:* x = -10
• Equation: 4x + 6 = 34
• Solution:* x = 7
• Equation: 4x - 6 = 34
• Solution:* x = 10
• Equation: -43 = 7 - 5x
• Solution:* x = 10
• Equation: -43 = 7 + 5x
• Solution:* x = -10
• Equation: -40 = 8 - 8x
• Solution:* x = 6

Additional Variations of Equations

• Equation: -4x - 1 = 15
• Solution:* x = -4
• Equation: x/5 + 3 = 10
• Solution:* x = 35
• Equation: -x/2 - 8 = 3
• Solution:* x = -22
• Equation: x/7 + 14 = 3
• Solution:* x = -77
• Equation: 7 - x = 5
• Solution:* x = 2
• Equation: -5 - x = 4
• Solution:* x = -9
• Equation: -3x - 5 = 7
• Solution:* x = -4
• Equation: 6x + 16 = -20
• Solution:* x = -6
• Equation: x/7 - 5 = -6
• Solution:* x = -7
• Equation: -6x + 2 = 14
• Solution:* x = -2

Final Group of Equations

• Equation: -3x - 7 = 8
• Solution:* x = -5
• Equation: 9 - x = 14
• Solution:* x = -5
• Equation: -x/3 - 5 = 1
• Solution:* x = -18
• Equation: -x/2 + 12 = -10
• Solution:* x = 44
• Equation: -2/3x + 4 = 8
• Solution:* x = -6
• Equation: -1/2x - 3 = -4
• Solution:* x = 2
• Equation: 4/5x + 5 = 17
• Solution:* x = 15
• Equation: -4/5x + 5 = 17
• Solution:* x = -15

Summary of Techniques

• Isolate the variable in two steps: first eliminate constants, then coefficient.
• Solutions can vary significantly based on the sign and coefficients of x.
• Forms include single-variable equations with positive/negative terms and fractions.