HSC Standard Math Practice Exam

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When solving an equation, what is an important step to maintain balance?

Add a number to one side only

Perform the same operation on both sides

Maintaining balance in an equation is crucial for finding the correct solution. When solving an equation, the principle of equality states that if you perform an operation on one side, you must perform the same operation on the other side to keep both sides equal.

For instance, if you have the equation \( x + 5 = 12 \) and you decide to subtract 5 from one side to isolate \( x \), you must also subtract 5 from the other side. This gives you \( x + 5 - 5 = 12 - 5 \), which simplifies to \( x = 7 \). Both sides of the equation remain balanced throughout the process, ensuring that the equality is preserved.

This principle applies to all mathematical operations—addition, subtraction, multiplication, and division. Without this step of performing the same operation on both sides, the equality can be disrupted, leading to incorrect solutions. Therefore, adhering to this operation is fundamental when solving equations in algebra.

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Subtract a number from one side only

Multiply only one side of the equation

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