s olving l iteral e quations and f ormulas lesson 2-5
TRANSCRIPT
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SOLVING LITERAL EQUATIONS AND
FORMULAS
Lesson 2-5
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A _______________ _______________ is an equation that involves two or more variables.
literal equation
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 = 12 + 2x
5y = 12 + 2x
Note: I work most of my literal equations vertically because often there are no like terms to line up when adding or subtracting.
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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
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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
2y
x a b
This is like doing the distributive property
in reverse
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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
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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 Name Formula Definitions of Variables
Perimeter of a rectangle P = 2l + 2w P = perimeter, l = length, w = width
Circumference of a circle C = 2πr C = circumference, r = radius
Area of a rectangle A = lw A = area, l = length, w = width
Area of a triangle A = ½ bh A = area, b = base, h = height
Area of a circle A = πr2 A = area, r = radius
Distance traveled d = rt D = distance, r = rate, t = time
Temperature C = degrees Celsius, F = degrees Fahrenheit
9
5
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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:
__________________________
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P = 2l + 2w
P – 2w = 2l + 2w – 2w
P – 2w = 2l
40 = l