Final answer:
To solve two-step equations with negatives, follow the rules for operation with negative numbers and apply inverse operations systematically. Start by isolating the term with the variable through addition or subtraction, then get the variable by itself via multiplication or division, always performing the same operations on both sides to maintain equality.
Step-by-step explanation:
To solve two-step equations with negatives, you need to apply the basic operations of addition, subtraction, multiplication, and division, keeping in mind how negative numbers affect the result. Let's go through these steps with an example equation: -3x + 4 = -2.
Understand the Rules for Negative Numbers
First, remember the rules for adding, subtracting, multiplying, and dividing negative numbers:
- When two numbers with the same sign add or multiply, the answer has a positive sign.
- When two numbers with opposite signs add, subtract the smaller number from the larger number, and give the answer the sign of the larger number.
- When subtracting, change the sign of the number being subtracted and follow the addition rules.
- The rules for multiplication apply to division as well.
Step-by-Step Solution
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- Add or subtract to isolate the term with the variable.
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- Multiply or divide to get the variable by itself.
Applying these steps to our example (-3x + 4 = -2):
1. Subtract 4 from both sides to isolate the term with the variable: -3x + 4 - 4 = -2 - 4, which simplifies to -3x = -6.
2. Divide both sides by -3 to get the variable by itself: -3x / -3 = -6 / -3, resulting in x = 2.
While working through the steps, always do the same operation to both sides to maintain the balance of the equation.