S OLVING L ITERAL E QUATIONS AND F ORMULAS Lesson 2-5

A _______________ _______________ is an equation that involves two or more variables. literalequation Rewriting a Literal Equation: A.–2x + 5y = 12 Solve for y. _________________________________ Add 2x to each side to “move” the x-term (You are trying to get “y” by itself.) _________________________________ Simplify _________________________________ Divide by 5 _________________________________ Simplify – 2x + 2x + 5y = x 5y = x Note: I work most of my literal equations vertically because often there are no like terms to line up when adding or subtracting.

B.a – 2b = –10 Solve for b. ________________________________ Subtract a from each side. ________________________________ Simplify ________________________________ Divide by –2 ________________________________ Simplify a – 2b – a = – 10 – a – 2b = – 10 – a

Factor each of the following expressions: C. – 3x – 9 = ____ (x + 3) D. 2xy + 6y = ____ (x + 3) E.9x – 18 = ____ (x – 2) F. ax – bx = ___ ( ____ – ____ ) – 3 2y xab This is like doing the distributive property in reverse

Rewriting a Literal Equation with only (mostly) Variables G.mx + 2nx = p Solve for x. ______________________________________ Use the distributive property to factor out the x _______________________________________ Divide both sides by ________. _______________________________________ Simplify x(m + 2n) = p m + 2n

Rewriting Formulas A formula is an equation that states a __________________ among quantities. Formulas are special types of ______________ _____________________ Some formulas you should know are on the table below: relationship literal equations Formula NameFormulaDefinitions of Variables Perimeter of a rectangleP = 2l + 2wP = perimeter, l = length, w = width Circumference of a circleC = 2πrC = circumference, r = radius Area of a rectangleA = lwA = area, l = length, w = width Area of a triangleA = ½ bhA = area, b = base, h = height Area of a circleA = πr 2 A = area, r = radius Distance traveledd = rtD = distance, r = rate, t = time TemperatureC = degrees Celsius, F = degrees Fahrenheit

I.Josh is planting a rectangular garden. The perimeter of the garden is 120 yd., and the width is 20 yd. What is the length of the garden? Solve the formula for length: Substitute the value of P and w: ______________________________________________________ __________________________ P = 2l + 2w P – 2w = 2l + 2w – 2w P – 2w = 2l 40 = l