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Solving Linear EQUATIONS

This guide covers the fundamentals of linear equations, defining what an equation is and exploring how to solve linear equations in one variable. We'll examine the general form of a linear equation, properties of equality, and solution sets. Key operations and inverse operations will be detailed, guiding you through the problem-solving process step-by-step. Additionally, we will touch on inequalities, providing examples of how to solve and graph them on a number line. This resource is ideal for those seeking clarity on linear equations and inequalities.

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Solving Linear EQUATIONS

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  1. Solving Linear EQUATIONS

  2. WHAT IS AN EQUATION? • A mathematical statement that two expressions is equivalent • Solution set of an equation is the value or values of the variable that make the equation true

  3. General form • Linear equation in one variable- general form is ax=b where a and b are constants • a is not equal to zero. • Examples: • 4x=8 • 3x-5=2

  4. Linear equation variables • The variable has no exponents, is not under a radical sign, and is not in the denominator of a fraction.

  5. Solving linear equations • Goal is to move everything with the variable to one side of the equation • Move everything without a variable to the other side of the equal sign • Must use properties of equality

  6. Properties of equality

  7. Properties of equality

  8. Solving linear equations • Isolate the variable • Perform the inverse, or opposite of every operation in the equation • What you do to one side you must do to the other • Inverse operations are done in the reverse order of PEMDAS • Add, subtract first, then divide or multiply to isolate the variable

  9. Solve • 3(2-3p)=42

  10. solve • -3(5-4r)=-9

  11. Solve • 3(w+7)-5w=w+12

  12. solve • 5(x-6)=3x-18+2x

  13. solve • 3(2-3x)=-7x-2(x-3)

  14. Solving inequalities

  15. inequalities • A statement that compares two expressions by using the <,> symbols. • The graph of an inequality is the solution set (the set of all points on the number line that satisfy the inequality) • Properties of Equality discussed earlier apply to inequalities

  16. The inequality difference • If you multiply or divide both sides by a negative number, you must reverse the inequality symbol

  17. solve • Solve and graph on an number line • 9x=4<12x-11

  18. solve • x+8

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