A Guide to the GRE/Working with Equations

Working with Equations An equation can be altered in any manner so long both sides are equally affected. An equation is a statement that two quantities are equal to each other. Anything can be done to an equation so long as it is done to both sides. x = 2y It is true that x is equal to 2 times y. 100x = 200y Multiplying both sides by 100 yields another true statement. x + 50 = 2y + 50 Adding 50 to both sides also yields another true statement. If there is a variable on both sides of an equation, consolidate it on one side. 3x - 12 = x + 2 - 2 -2 Subtract 2 from both sides 3x - 14 = x -x -x Subtract x from both sides 2x - 14 = 0 + 14 + 14 Add 14 to both sides 2x = 14 ÷ 2 ÷ 2 Divide both sides by 2 x = 7 In an inequality (such as x < y), the same rules of equations apply, except that when multiplying both sides of an inequality by a negative number, the inequality sign must be flipped around. For example, if a > b, then -a < -b. Practice Solve for the variable in the following equations. 1. 6x - 4 = 1 + x 2. 2a = 3. 3h - 17 = h + 4 Answers to Practice Questions 1. x = 1 6x - 4 = 1 + x Take the initial equation. 6x = 5 + x Add 4 to both sides. 5x = 5 Subtract x from both sides. x = 1 Divide both sides by 5. 2. a = 2a = Take the initial equation. 2a2 = 16 Multiply both sides by a. a2 = 8 Divide both sides by 2. a == Take the square root of both sides. 3. h = 10.5 3h - 17 = h + 4 Take the initial equation. 3h = h + 21 Add 17 to both sides. 2h = 21 Subtract h from both sides. h = 10.5 Divide both sides by 2.