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.
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.