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Solving Literal Equations
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Solving Literal Equations

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  • I need help solving these equations: SOLVE for X . . . ax + b + a(x + b) = b, a(x + c) + b(x + d) - ax = e, 3x - (x + n) = m, SOLVE for P. . . P/6rn = 7/9nx, f + P/3 = P/8, 2P/m - r/s = Ps + q/ms

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  • 1. 1.5: Literal Equations
    • Goals:
    • Solve equations for a specific variable
    • Evaluate equations for a specific variable
  • 2. Review What it means to solve equations:
    • To solve an equation for x means to get x by itself on one side of the equation.
    • ( x = _____ )
    • To solve an equation for y means to get y by itself on one side of the equation.
    • ( y = _____ )
    • Therefore, to solve for any variable is to get it by itself on one side of the equation.
  • 3. What are Literal Equations?
    • A literal equation is an equation with more than one variable.
    AREA BASE HEIGHT
  • 4. Rules to Solving Literal Equations Solving equations for a specific variable involve the same rules as solving an equation.
    • Simplify each side of the equation, if needed, by distributing or combining like terms.
    • 2. Move the variable being solved for to one side of the equation by using the opposite operation of addition or subtraction.
    • 3. Isolate the variable being solved for by itself by applying the opposite operation to each side.
      • a. First , use the opposite operation of addition or subtraction to move any other constants or variables to the other side.
      • b. Second , use the opposite operation of multiplication or division to eliminate the coefficient of the variable being solved for.
  • 5. Example: Solve the following for y In other words, isolate the variable “ y ” by itself Undo the subtracting 5x by adding 5x to both sides. Undo the multiplying by 2, by dividing both sides by 2 Remember, all numbers on the other side get divided by 2. Since you have “ y = “, you have now solved for y
  • 6. Example: Solve the same equation for x In other words, isolate the variable “ x ” by itself Undo the positive 2y by subtracting 2y from both sides. Undo the multiplying by -5, by dividing both sides by -5 Remember, all numbers on the other side get divided by -5. Since you have “ x = “, you have now solved for x Move the negative to the numerator by changing all the signs.
  • 7. Formula Examples:
    • Solving literal equations allows you to transform formulas (such as area, volume, perimeter, etc) so you can solve for any of the parts:
    Solve the following formula for “ r ”
  • 8. Formula Examples:
    • Since “r” is being multiplied by both the “2” and “  ” you would divide by “ 2  ”
    Solve the following formula for “ r ”
  • 9. Formula Examples:
    • Since the equation now reads:
    • “ r = “
    • the equation is solved.
    Solve the following formula for “ r ”
  • 10. Solve the following formula, the perimeter of a rectangle for “ w ” In other words, isolate the variable “ w ” by itself Undo the positive “2 l ” by subtracting “2 l ” Undo the multiplication by dividing both sides by 2 Remember, all the numbers get divided by 2
  • 11. Examples: On Your Own 1) ; Solve for b 2) ; Solve for y 3) ; Solve for y
  • 12. Examples: On Your Own
    • 1) Solve for b:
    • A = ½bh
    • 2) Solve for y:
    • 3(x-4y) = 24
    • 3) Solve for y:
    • 5xy + 2z = 10
  • 13. Examples: On Your Own
    • 1) Solve for b:
    • A = ½bh
    • 2) Solve for y:
    • 3(x-4y) = 24
    • 3) Solve for y:
    • 5xy + 2z = 10
  • 14. Examples: On Your Own
    • 1) Solve for b:
    • A = ½bh
    • 2) Solve for y:
    • 3(x-4y) = 24
    • 3) Solve for y:
    • 5xy + 2z = 10

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