Isolate an indicated variable in an equation. Literal Equations Isolate an indicated variable in an equation.

Solve Literal Equations Our goal is to rearrange equations or formulas to isolate a desired variable by using inverse operations (just as you would use to solve an equation) However you won’t end up with variable=constant number (like x=7), you will end with variable=expression (like r = 𝑑 𝑡 ) Use the properties of algebra to do this “legitimately.”

Solve for u. Give a property to justify each step Solve for u. Give a property to justify each step. (Means isolate “u” in the following equations ) 1/3u – 8 = y 1/3u = y + 8 u = 3(y + 8) *That is the final answer. All you have to do is isolate the indicated variable. You will not end up with u=number.* w = 9 + 14ux w – 9 = 14ux (w – 9) = u 14x *This is the final answer. You are isolating the variable and will still have other variables in the equation* Addition Property (add 8) Multiplication Property (•3) Subtraction Property (- 9) Division Property (÷ 14x)

Isolate “w” in the following equations Isolate “w” in the following equations. Give a property to justify each step. y = 2x + w v vy = 2x + w vy – 2x = w w + x = y 3 w = y – x 3 w = 3(y – x) Multiplication Property (•v) Subtraction Property (-2x) Subtraction Property (-x) Multiplication Property (•3) Image from http://varner.typepad.com/mendenhall/

k = am + 3mx k = m(a + 3x) k = m a + 3x Isolate “m” in the following equation. Give a property to justify each step. The “m” is in both terms. It is a factor of both terms. You will need to “factor it out of them.” This is the distributive property backwards. Distributive Property Division Property (÷ [a + 3x]) k = am + 3mx k = m(a + 3x) k = m a + 3x Image from http://varner.typepad.com/mendenhall/

Formulas Solve for h V = 𝟏 𝟑 𝝅 𝒓 𝟐 h Image from http://varner.typepad.com/mendenhall/ There are many formulas that you have used so far in your math career. Here are a few: D = rt A = bh I = Prt V = LWH SA = 2LW + 2LH + 2WH V = 1 3 𝜋 𝑟 2 h Solve for h V = 𝟏 𝟑 𝝅 𝒓 𝟐 h 3V = 𝜋 𝑟 2 h Mult. Prop of Eq. (By 3 to clear fraction) 3V = h Division Prop. of Eq. 𝝅 𝒓 𝟐