Transcript MTH 100 Linear Equations In One Variable

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