An equation is a statement that two expressions have equal value, with the equal sign expressing a relationship between the entire left and right sides rather than signaling “the answer.” This understanding includes recognizing that an equation may be true or false for particular values, and that a variable represents a number whose value can make the equality true; it supports equivalent transformations and solving equations with rational numbers.
An equation says that the entire expression on the left has the same value as the entire expression on the right. The equal sign does not mean “the answer comes next.”
For example, consider
Suppose . To check whether this value makes the equation true:
Substitute for :
Simplify the left side:
Compare both sides:
Both sides have the same value, so makes the equation true. We say that is a solution to the equation.
If , the equation becomes
which simplifies to
This is false because the two sides do not have equal values. Thus, is not a solution.
When reading an equation, always treat the left side and right side as two quantities that must be equal.
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