Advance Algebra with Trigonometry, Section 2-1: Linear Equations in One Variable

Advance Algebra with Trigonometry

​Section 2-1: Linear Equations in One Variable

by Jeremy Adelmann

​Section 2-1 Objectives

​​Students will be able to:

• ​Decide whether a number is a solution of a linear equation.

• ​Solve linear equations by using the addition and multiplication properties of equality.

• ​Solve linear equations by using the distributive property.

• ​Solve linear equations with fractions or decimals.

• ​Identify conditional equations, contradictions, and indentities.

​Objective 1: Decide whether a number is a solution of a linear equations.

​If the variable in an equation can be replaced with a real number that makes the statment true, the that number is a solution of the equation.

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​7 is a solution for the equation 

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​An equation is solved by finding its solution set. The solution set for this equation is {7}.

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​If multiple equations have the same solution set, then they are Equivalent Equations. The solution set is {2}

​Objective 2: Solve linear adding and mutiplying

​Solve 5x - 3x - 6 = 14 + 8x + 4.

​The goal is to isolate the variable on one side of the equation.

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​Combine Like Terms

Add 6 to both sides

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Subtract 8x from both sides

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​Divide both sides by -6

​Solving a Linear Equation in One Variable

• ​Step 1: Clear Fractions - Eliminate any fractions by muliplying each side by the least common denominator.

• ​Step 2: Simplify each side separately - Use distributive property to clear parantheses and combine like terms as needed.

• ​Step 3: Isolate the variable terms on one side. Use the addition property to get all terms with variables on one side of the equation and all numbers on the other.

• ​Step 4: Isolate the varaible - Use the multiplication property to get an equation with just the variable (coefficient of 1) on one side.

• ​Step 5: Check - Substitute the proposed solution into the original equation.

​Objective 3: Using the Distibutive Property

​Solve 2(k - 5) + 3k = k + 6

• ​Since there are no fractions, Step 1 does not apply.

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Distributive Property

Multiply

Combine Like Terms

Add 10 to both sides

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Subtract k from both sides

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Divide both sides by 4

​Obj. 4: Solving Linear Equations w/ Fractions

​Solve

​

​Start by eliminating the fractions. Multiply both sides by the LCD, 6.

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​The LCD is 6.

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​ Distributive Property

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​ Multiply;

​Obj. 4: Solving Linear Equations w/ Fractions

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​Distributive Property

​Multiply

​Combine Like Terms

​Add 17 to both sides

​Combine Like Terms

​Divide both sides by 7