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Solving Linear Equations

Solving Linear Equations. Using Multiplication/Division. Solving 1-Step Equations. To find the solution to an equation we must isolate the variable. We isolate the variable by performing operations that will eliminate (cancel) the other numbers from the expression.

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Solving Linear Equations

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  1. Solving Linear Equations Using Multiplication/Division

  2. Solving 1-Step Equations • To find the solution to an equation we must isolate the variable. • We isolate the variable by performing operations that will eliminate (cancel) the other numbers from the expression. • The Multiplication Property of Equality says that we can multiply the same number on both sides of an equation without changing the solution to the equation.

  3. Multiplication Property of Equality • Take the equation: 3x = 15 • Our goal is to multiply a number on both sides of the equation that will isolate the x by canceling the coefficient of x, 3. • Since 3 and x are multiplied, we don’t want to cancel 3 to a zero, we want to cancel 3 to a value of one. (Perform an operation that will make 3x become 1x = x.)

  4. Reciprocals multiply to 1. Multiplication Property of Equality • What number, when multiplied by 3, will give us one? • The Multiplication Property of Equality says we can multiply 1/3 to the equation as long as we multiply it on both sides.

  5. Inverse Property of Mult. says that reciprocals multiply to 1. Multiply fractions. Identity Property of Mult. Says that 1x = x. Multiplication Property of Equality • See what happens: Multiply 1/3 on both sides of the equal sign.

  6. Checking the Solution • Always check the solution by substituting the value back into the original equation. 3x = 15 3 • 5 = 15 15 = 15 • The sentence should be true.

  7. Solving by Multiplication • Multiply both sides of the equation by the number that will cancel with the coefficient of the variable. This will isolate the variable by making its coefficient the number 1. • Reciprocals multiply to 1. The reciprocal of a whole number is 1 over the number.

  8. √ Examples Multiply 3/2 on both sides of the equal sign. Check:

  9. √ Examples Multiply 1/4 on both sides of the equal sign. Check:

  10. √ Examples w/5 is the same thing as 1/5 • w, multiply both sides by 5/1. Check:

  11. Try These!

  12. Solutions!

  13. Solutions!

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