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1.4 Solving Linear Equations

Learn how to solve linear equations, understand equivalent equations, apply properties of equality, and solve various equation types with step-by-step examples. Master the fundamentals of algebra with this informative guide.

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1.4 Solving Linear Equations

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  1. 1.4 Solving Linear Equations • A __________ ____________ in one variable x is an equation that can be written in the form where a and b are real numbers, and a ≠ 0.

  2. Solving an Equation • Solving an equation in x involves determining all values of x that result in a _________statement when substituted into the equation. • Such values are called ____________, or ________ of the equation.

  3. Equivalent Equations • Equivalent equations are two or more equations that have the same ____________________. • For example, , , and are equivalent equations because the solution set for each is {-3}.

  4. Properties of equality • The addition property of equality: • The same real number or algebraic expression may be added to both sides of an equation without changing the equation’s _____________ _______. • The multiplicative property of equality: • The same nonzero real number may multiply both sides of an equation without changing the equation’s ______________ _______.

  5. Using Properties of Equality to Solve Linear Equations add 3 to both sides divide both sides by 6 (or multiply by ____ )

  6. Example 1: • Solve and check

  7. Steps for Solving a Linear Equation • _____________ the algebraic expression on each side by removing grouping symbols and combining like terms. • Collect all the _________ terms on one side and all the numbers, or constant terms, on the other side. • Isolate the __________ and solve. • Check the proposed solution in the ___________ equation.

  8. Example 2: • Solve and Check

  9. Example 3: • Solve and Check:

  10. Example 4: • Solve and check:

  11. Types of Equations • An equation that is true for all real numbers for which both sides are defined is called an __________. • An equation that is not an identity, but that is true for at least one real number, is called a _______________ equation. • An ________________ equation is an equation that is not true for even one real number.

  12. Example 5: • Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation

  13. Example 6: • Solve and determine whether the equation is an identity, a conditional equation, or an inconsistent equation.

  14. Example 7: The formula N = 0.12x + 0.4 models the of new motorcycles sold in the United States, N, in millions, x years after 1998. When will new motorcycle sales reach 1.6 million?

  15. Homework: Page 46 1 – 49 odds 25 total

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