SOLVING LITERAL EQUATIONS Bundle 1: Safety & Process Skills

Solving Literal Equations  An equation is a mathematical sentence with an equal sign.  The solution of an equation is a value for a variable that makes an equation true. You can substitute a number for a variable to determine whether the number is a solution of the equation.  A Literal Equation is an equation with more than one variable.  Examples: Is the given number a solution for the equation? Ex) x = 200, for x=30 Ex) 3 = 12 – a, for a=6 YES! NO!

Solving Multi-Variable Equations  A. Important Rules for Solving Equations  Rule #1) When you solve an equation, your goal is to get the variable on one side of the equal sign, by itself, and positive. In other words, you are trying to isolate the variable.  Rule #2) When you are solving for a variable, you MUST use the opposite or inverse operations to isolate the variable on one side of the equation.  Rule #3) Whatever you do to one side of an equation, you MUST do to the other side of the equation. In other words, you must keep the equation equal/balanced.

Solving Multi-Variable Equations  Think of solving an equation like lifting weights. If you add or subtract weight from one side of the barbell, you must add or subtract the same amount of weight from the other side of the barbell to keep it balanced.

Solving Multi-Variable Equations B. Solving Equations by Adding or Subtracting  When you are solving an equation, you MUST use the inverse operation to isolate the variable on one side of the equation.  REMEMBER: If you add or subtract a number from one side of the equation, you must add or subtract the same number from the other side of the equation.  You can only add or subtract terms with the same variable parts!  Examples: 2x + 3x = 5x4y – 3y = y1 + 7 = 8 But 2x +3 is NOT EQUAL TO 5x. The 2 terms don’t have the SAME VARIABLE PART! What about 4 – 3x? 5x – 2y?xy + ab – 1?

Solving Multi-Variable Equations  Whenever you see a variable, it is understood to have a 1 in front of it. This is called the IMPLIED one and it is multiplied by the variable.  Examples:  Directions: Solve each equation for the variable.  Ex) x + 4 = 6 *You can always check to see if your answer is correct by substituting it back into the original equation.  Ex) 2t = t + 2  Ex) – 14 = y – 7 Ans: x = 2 Ans: t = 2 Ans: y = – 7

Solving Multi-Variable Equations C. Solving Variations of One-Step Equations by Multiplying or Dividing  When you are solving an equation, you MUST use the inverse operation to isolate the variable on one side of the equation.  REMEMBER: If you multipy or divide a number from one side of the equation, you must multiply or divide the same number from the other side of the equation.  The sign on the number MATTERS! Whenever you see a negative sign in front of a number or variable, it is understood to have a negative 1 in front of it.

Solving Multi-Variable Equations  Examples  Directions: Please rewrite each variable, expression, or equation so that the number in front of each variable is visible. Then solve each equation for the variable.  Ex) –y + 1 = 5  Ex) –x = –12 + x  Ex) d + 14 = –6d  Ex) –t + 5= 9  Ex)

Solving Multi-Variable Equations  Examples  Directions: Please rewrite each variable, expression, or equation so that the number in front of each variable is visible. Then solve each equation for the variable.  Ex) –y + 1 = 5  Ex) –x = –12 + x  Ex) d + 14 = –6d  Ex) –t + 5= 9  Ex) Ans: y = – 4 Ans: x = 6 Ans: d = – 2 Ans: t = – 4 Ans: x = 3

Solving Multi-Variable Equations  What do you do differently when there is more than one variable? NOTHING!  The rules for solving an equation with ONE VARIABLE are the same when the equation has MULTIPLE VARIABLES.  Example: Solve this equation for y.  9x – 3y = 6  9x – 9x – 3y = – 9x + 6 Subtract 9x from both sides  – 3y/– 3 = (– 9x + 6)/– 3 Divide both sides by – 3  y = 3x – 2 FINAL ANSWER!

Solving Multi-Variable Equations  What about when the equation is ALL variables?  Nothing Changes! Same rules apply to all equations.  Example: Solve this equation for m.  Multiply both sides by V.  Final Answer

Solving Multi-Variable Equations  Example: Now solve the same equation for V. Multiply both sides by V. Divide both sides by D. Final Answer

Your Turn!  Now its time for you to practice solving equations for a variable.