How to Solve Linear Equation Expressions With Parenthesis

Simplify an expression inside parentheses before solving the rest of an equation.

To solve an equation that contains parentheses, you must solve the expressions inside the parentheses before solving the rest of the equation. The order of operations in mathematics dictates that you must solve an equation or expression in the following order: parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right. You must perform each operation in order before moving to the next operation to solve an equation. If you solve an equation in an order other than the order of operations, you may get an incorrect answer.

Instructions

1. Determine an equation that contains parentheses. For the following example, use the equation 2(x - 5) + 2 = (2^2 + 2).

2. Simplify the expressions inside the parentheses because parentheses come first in the order of operations. In the example, the expression on the left side of the equation cannot be simplified because it has unlike terms, so simplify the expression inside the parentheses on the right side of the equation using the order of operations on the expression. Calculate 2 squared because exponents come before addition in the order of operations. This equals 4, which leaves 2(x - 5) + 2 = (4 + 2).

3. Add the remaining terms inside the parentheses. In the example, add 4 and 2, which equals 6. This leaves 2(x - 5) + 2 = 6.

4. Multiply any terms in the equation that can be multiplied from left to right because multiplication is the next applicable operation in the order of operations. In the example, distribute the 2 that's outside the parentheses by multiplying it by each term inside the parentheses -- 2 times x equals 2x, and 2 times -5 equals -10. This leaves 2x - 10 + 2 = 6.

5. Add and subtract any terms in the equation that can be added or subtracted from left to right because addition and subtraction are the next operations in the order of operations. In the example, add -10 and 2, which equals -8. This leaves 2x - 8 = 6.

6. Add or subtract any remaining terms from left to right. In the example, add 8 to both sides of the equation to simplify the equation. This results in 2x - 8 + 8 = 6 + 8, which leaves 2x = 14.

7. Isolate x on the left side of the equation to solve for x. In the example, divide both sides of the equation by 2 to isolate x on the left side of the equation. This results in 2x/2 = 14/2, which leaves x = 7. This is the solution to the equation with parentheses.

Tips & Warnings

• Check your answer by substituting it for "x" in the original equation, solving the equation and verifying that both sides of the equation are equal.

• Be sure to use the order of operations on each individual expression inside parentheses.

References

• University of North Texas Department of Mathematics: Order of Operations
• Kirkwood Community College: Review of Linear Expressions and Equations