SOLVING LITERAL EQUATIONS. Bundle 1: Safety & Process Skills
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1 SOLVING LITERAL EQUATIONS Bundle 1: Safety & Process Skills
2 Solving Literal Equations An equation is a atheatical sentence with an equal sign. The solution of an equation is a value for a variable that akes an equation true. You can substitute a nuber for a variable to deterine whether the nuber is a solution of the equation. A Literal Equation is an equation with ore than one variable. Exaples: Is the given nuber a solution for the equation? Ex) x = 200, for x=30 Ex) 3 = 12 a, for a=6 YES! NO!
3 A. Iportant 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 ust keep the equation equal/balanced.
4 Think of solving an equation like lifting weights. If you add or subtract weight fro one side of the barbell, you ust add or subtract the sae aount of weight fro the other side of the barbell to keep it balanced.
5 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 nuber fro one side of the equation, you ust add or subtract the sae nuber fro the other side of the equation. You can only add or subtract ters with the sae variable parts! Exaples: 2x + 3x = 5x 4y 3y = y = 8 But 2x +3 is NOT EQUAL TO 5x. The 2 ters don t have the SAME VARIABLE PART! What about 4 3x? 5x 2y? xy + ab 1?
6 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 ultiplied by the variable. Exaples: Directions: Solve each equation for the variable. Ex) x + 4 = 6 Ans: x = 2 *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: t = 2 Ans: y = 7
7 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 ultipy or divide a nuber fro one side of the equation, you ust ultiply or divide the sae nuber fro the other side of the equation. The sign on the nuber MATTERS! Whenever you see a negative sign in front of a nuber or variable, it is understood to have a negative 1 in front of it.
8 Exaples Directions: Please rewrite each variable, expression, or equation so that the nuber 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) 1 = 3 x
9 Exaples Directions: Please rewrite each variable, expression, or equation so that the nuber 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 Ans: y = 4 Ans: x = 6 Ans: d = 2 Ans: t = 4 Ex) 1 = 3 x Ans: x = 3
10 What do you do differently when there is ore than one variable? NOTHING! The rules for solving an equation with ONE VARIABLE are the sae when the equation has MULTIPLE VARIABLES. Exaple: Solve this equation for y. 9x 3y = 6 9x 9x 3y = 9x + 6 Subtract 9x fro both sides 3y/ 3 = ( 9x + 6)/ 3 Divide both sides by 3 y = 3x 2 FINAL ANSWER!
11 What about when the equation is ALL variables? Nothing Changes! Sae rules apply to all equations. Exaple: Solve this equation for. D = V D V = V V Multiply both sides by V. D V = Final Answer
12 Exaple: Now solve the sae equation for V. D = V D V = V V D V = Multiply both sides by V. D V D = D Divide both sides by D. V = D Final Answer
13 Your Turn! Now its tie for you to practice solving equations for a variable.
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