SAT New Math: Topic 1. Heart of algebra:1.1 Linear Equations

Key Facts

1. An equation involving only one variable of degree 1 (power of the variable does not exceed 1) is called a linear equation.
2. The value of the variable that makes both the sides of the equation equal is called the solution or root of the equation.
3. The equation remains unchanged by
(i) adding the same number to both the sides of an equation or
(ii) subtracting the same number from both the sides of the equation or
(iii) multiplying both the sides of the equation by the same non-zero number or
(iv) dividing both the sides of the equation by the same non-zero number.
4. Transposing a term from LHS to RHS changes the sign of the term from (+ve) to (–ve) and (–ve) to (+ve).
5. To Solve a linear equation in one variable, take all the terms involving the variable on one side and the constant terms to the other. Reduce the equation to the from cx = d, where \(x=\frac{c}{d}\)

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