* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Solving First-Degree Equations Containing Fractions
Path integral formulation wikipedia , lookup
Debye–Hückel equation wikipedia , lookup
Unification (computer science) wikipedia , lookup
Two-body Dirac equations wikipedia , lookup
Two-body problem in general relativity wikipedia , lookup
Schrödinger equation wikipedia , lookup
BKL singularity wikipedia , lookup
Van der Waals equation wikipedia , lookup
Itô diffusion wikipedia , lookup
Maxwell's equations wikipedia , lookup
Calculus of variations wikipedia , lookup
Euler equations (fluid dynamics) wikipedia , lookup
Equation of state wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Navier–Stokes equations wikipedia , lookup
Schwarzschild geodesics wikipedia , lookup
Equations of motion wikipedia , lookup
Differential equation wikipedia , lookup
Math 952 4.5 "Solving Equations with Fractions" Objectives: * Understand that fractions and mixed numbers are possible solutions to equations. * Learn how to solve equations with fractional coe¢ cients. Preliminaries: In Section 1.5, we discussed solving …rst-degree equations with whole number constants and coe¢ cients. In Section 2.7, we did it with integers. Today, we’ll solve equations having fractions as coe¢ cients. De…nition: "First-Degree Equation in x" A …rst degree equation in x (or linear equation in x) is any equation that can be written in the form where a, b; and c are constants and a 6= 0. ; Solutions of a First-Degree Equation: A …rst-degree equation has exactly : Solving First-Degree Equations Containing Fractions Example 1 (Using the addition and multiplication principle) Solve each equation. a) x + 10 = 22 b) 5y 2y = 30 To Understand How to Solve Equations: 1: Apply the distributive property to remove parentheses whenever necessary. 2: Combine like terms on each side of the equation. 3: If a constant is added to a variable, add its opposite to both sides of the equation. 4: If a variable has constant coe¢ cient other than 1, divide both sides by that coe¢ cient. 5: Generally, use the Addition Principle …rst so that terms with variables are on one side and constant terms are on the other side. Then combine terms and use the Multiplication Principle. 6: Remember that the object is to isolate the variable on one side of the equation with a coe¢ cient of 1. Example 2 (Using both principles) Solve the following equations. a) 4x + 22 = 18 b) 2 (x Page: 1 5) + 3x = 20 Notes by Bibiana Lopez Prealgebra by Franklin Wright 4.5 Equations with Fractions Special Note on Fractional Coe¢ cients: An expression such as 51 x can be thought of as a product. Similarly, NOTE: To solve equations where the variable has a fractional coe¢ cient (as above) we multiply both sides by the reciprocal of the coe¢ cient. Example 3: (solving equations with fractional coe¢ cients) Solve the equations. 3x a) + 2 = 17 4 c) 3x 2x + = 5 5 1 10 b) d) Page: 2 23 = 2 n 5 1 y 2 2 n= 3 3 4 Bibiana Lopez Prealgebra by Franklin Wright 4.5 NOTE: More general equations with fractional coe¢ cients can be solved by …rst multiplying every term in the equation by the LCM of all denominators. Example 4: (solving equations with fractional coe¢ cients) Solve each equation. 3 1 3 a) x x= 4 3 8 b) Page: 3 1 1 4 = x+ 2 3 15 Bibiana Lopez