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MTH 100 Linear Equations In One Variable Objectives 1. Determine if a Given Value is a Solution to a Linear Equation. 2. Solve Linear Equations in One Variable. 3. Identify Contradictions and Identities. Objective 1 • A given value is a solution to a linear equation if substituting that value into the equation results in a true statement (the same value on both sides of the equal sign). Objective 1 Example • Determine if the given value is a solution to the corresponding linear equation. t = 4; 6(t + 1) – t = 7t – 2 Objective 2 • Solving a linear equation in one variable typically involves isolating the variable. • Steps in the process: 1. Eliminate fractions by multiplying by the LCD. 2. Use the distributive property to eliminate parentheses. 3. Combine like terms on either side of the equation. 4. Move variable terms to one side, non-variable terms to the other. 5. Divide both sides by the coefficient of the variable term. Objective 2 Examples 11 2 x 9 4 x 10 7 x 3( x 1) 6 x ( x 10) 2 x 3 1 1 y ( y 1) 5 y 4 5 Objective 3 • A contradiction is an equation with no solutions. In a contradiction: 1. All the variables cancel out. 2. The resulting statement is false. • An identity is an equation with infinitely many solutions. In an identity: 1. All the variables cancel out. 2. The resulting statement is true. Objective 3 Examples 7(m 6) 2m 5(m 8) 2 5n 4 9n 5(n 2) 9n