Solving Multi-Step Equations
Concept
The term “multi” means many or more than two. Therefore, a multi-step equation can be defined as an algebraic expression that requires several operations such as addition, subtraction, division, and exponentiation to be solved. Multi-step equations are solved by applying similar techniques used in solving one-step and two-step equations.
Like we saw in one-step and two-step equations, the main objective of solving multi-step equations is to isolate the unknown variable on either the RHS or LHS of the equation while keeping a constant term on the opposite side. The strategy of obtaining a variable with a coefficient of one entails several processes.
The Law of equations is the most important rule you should remember while solving any linear equation. This implies that, whatever you do to one side of the equation, you MUST do to the opposite of the equation.
Rules
1. Eliminate any grouping symbols such as parentheses, braces, and brackets by employing the distributive property of multiplication over addition.
2. Simplify both sides of the equation by combining like terms.
3 Isolate a variable on any side of the equation depending on your preference.
4. A variable is isolated, performing the two opposite operations, such as addition and subtraction followed by multiplication and division.
Example
Solve for k.
3(k – 2) + k = 5(k + 3) – 9
Solution
3(k – 2) + k = 5(k + 3) – 9
3k – 6 + k = 5k + 15 – 9
4k – 6 = 5k + 6
4k – 5k = 6 + 6
-k = 12 or k = -12
Practice Solving Multi-Step Equations
Practice Problem 1
Solve for c.
7(c – 5) – 3c = 4(2c + 3) – 11
Practice Problem 2
Solve for d. If necessary, round to the nearest tenth.
2.1(d + 7) – 30.5d = -21(d – 1) + 12.2
Practice Problem 3
Aiden found a big bag of table tennis balls in a clearance bin at a sports store. When she opens the bag to see how many tennis balls are in the bag, the bag breaks, sending the balls in several directions. Two-thirds of the balls rolled onto the floor, one-sixth landed in her lap, one-twelfth rolled under her bed and 3 were still in the bag. How many tennis balls were in the unopened bag?
Variable: A symbol, usually a letter, used to represent a number in mathematical expressions or sentences.
Equation: A mathematical sentence stating that two quantities are equal.
One-Step Equation: An equation that contains one operation.
A two-step equation is an algebraic equation that takes you two steps to solve.
Multi-step equations are algebraic expressions that require more than one operation, such as subtraction, addition, multiplication, division, or exponentiation, to solve.
Distributive Property – to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses.
Related Skills
Direct Variation Equations (y = mx)
Slope-intercept Form of an Equation
Graphing Lines Using Intercepts
Write Linear Equations
Solutions of Systems of Equations
Solve Linear Systems of Equations by Graphing
Solve Systems of Equations by Substitution
Solve Systems of Equations by Elimination
Applications of Systems