Digital SAT · Math · Algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A linear equation in one variable has x only to the first power. To solve it, do the same thing to both sides until x stands alone: expand parentheses, clear fractions, collect the x terms on one side and the numbers on the other, then divide.
In a word problem, name the unknown, turn the sentence into an equation, then solve. A fixed fee is a number on its own; a rate is multiplied by the unknown.
Some questions ask how many solutions there are. Simplify both sides and compare. If the x terms differ, there is one solution. If the x terms match, the equation has either no solution or infinitely many, depending on the constants.
Multiplying only part of an equation when clearing fractions or expanding parentheses. Multiply every term, and take care with a minus sign in front of parentheses: −2(x − 3) = −2x + 6.
Answer: x = 7
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