Algebra is a critical component of the GMAT, particularly in the Problem Solving section. This section tests your ability to manipulate algebraic expressions, solve equations, and understand functions.

• Variables: Symbols that represent numbers in equations. For example, in the equation $x + 5 = 10$, $x$ is a variable.
• Equations: Mathematical statements that assert the equality of two expressions. For instance, $2x + 3 = 7$ is an equation.
• Functions: A relation between a set of inputs and a set of possible outputs. For example, $f(x) = 2x + 3$ defines a function.

To solve a linear equation, isolate the variable on one side of the equation. For example:

Given the equation $3x - 9 = 0$, we can solve for $x$ as follows:

1. Add 9 to both sides: $3x = 9$
2. Divide both sides by 3: $x = 3$

Solve the equation $4x + 7 = 3x + 12$.

1. Subtract $3x$ from both sides: $4x - 3x + 7 = 12$
2. Simplify: $x + 7 = 12$
3. Subtract 7 from both sides: $x = 5$

The solution is $x = 5$.

Solve the following equation:

$2(x - 3) = 4x - 10$

1. Distribute on the left side: $2x - 6 = 4x - 10$
2. Subtract $2x$ from both sides: $-6 = 2x - 10$
3. Add 10 to both sides: $4 = 2x$
4. Divide by 2: $x = 2$

The solution is $x = 2$.

Mastering algebra is essential for success on the GMAT. Practice solving equations and manipulating expressions to improve your problem-solving skills.