Brittany's Algebra II Webpage
Solving
Linear Equations
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3-2x = 4
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Linear Equations-Have
one variable.
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2x+11=15-6x
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You can use properties of
real numbers and transformations that produce equivalent equations to solve
linear equations.
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Now SOLVE:
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-2(x-4)=12
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FIRST you will distribute
the -2 to what's in the parenthesis.
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-2x+8=12
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THEN subtract the 8 from
both sides. (The -8 will cancel out with the 8 because they are like terms.)
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-2x = 4
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NEXT you will divide the
-2 from both sides. (Once again the -2 and -2 will cancel out because they
are like terms.)
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x = -2
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NOW you have the answer,
but don't forget to CHECK!
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CHECK:
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-2(-2-4) = 12
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To CHECK you will substitute
the -2 in for x.
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-2(-6) = 12
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Then SOLVE with the substitute.
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12 = 12
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Our answer checks!!!!
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Now lets try something a little
harder!
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-12x+4 = -10x+40-14x
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First we want to add all
of the like terms. (Remember that you can only add like terms on the same
side of the = sign!)
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-12x+4=-24x+40
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Then we will get all the
x's on the same side. So we will subtract 4 from the 40.
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-12x = -24x+36
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Now we will add 24 to the
-12.
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12x = 36
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Take the 12 and divide it
into the 36.
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x = 3
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NOW you have x = 3!!!
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CHECK....
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-12(3)+4=-10(3)+40-14(3)
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Substitute the 3 in for
x.
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-36+4=-30+40-42
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Follow the order of operations
and do your multiplication first.
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-32=10-42
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Then still following the
order of operations we add and sutract.
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-32 = -32
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Our problem checks!!
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Solving Literal Equations:
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D=MV
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Literal Equations have more
than one variables.
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???
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A numerical answer is NOT
available for this type of equation! (Formulas are an example of literal
equations.)
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NOW LET'S TRY ONE!!
Solve...
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E=IR
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Solve for I (voltage)
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E=IR
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We need to get I by it's
self. So we divide E by R and get...
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E/R=I
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That's all you do!
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Now Let's Try Another!
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C=Q/V
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Solve for V (capacitance).
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C=Q/V
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We need to multiply V by
both sides. (Of course it cancels out on one side.)
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CV=Q
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Now we have our answer!
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NOW FOR SOMETHING HARDER!
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F=G(Mm/r2
)
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Solve for G (gravitational
force).
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F=G(Mm/r2
)
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Now we need to get the G
by itself. So we multiply r2 to the F.
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Fr2=G(Mm)
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Now we need to divide the
Mm to the Fr2.
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Fr2/Mm=G
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Now we have our answer!!!
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How to write an equation for
a line in three ways:
Slope-intercept form:
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y=mx+b
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In Slope-intercept form
you are given the slope (m) and the y-intercept (b), use this equation.
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Now let's try a problem!!
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m=1 b=2
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All you haft to do is substitute
these numbers into the formula above!
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y=1x+b
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And that's how you get the
slope-intercept form!
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Point-slope form:
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y-y1=m(x-x1)
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In Point-slope form you
are given the slope (m) and a point (x1,y1), use
this equation!
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Time for an example!
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m=5 , (10,15)
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This is what you are given!
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y-15=5(x-10)
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Now you will substitue the
given from the line above!THIS IS YOUR ANSWER IN POINT-SLOPE FORM!(You
can keep going to get the Slope-intercept form.)
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y-15=5x-50
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Then you will distribute!
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y=5x-35
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Then you will add 15 to
both sides and come up with the Slope-intercept form.
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Standard:
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ax+by=c
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In the Standard form you
use this equation. Using this form you can figure out the x and y-intercepts!
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You guessed now it's time to
try one!
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y=2x+4
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This is what you are given
to figure out the standard form!
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y-4=2x
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Now we need to get both
variables onthe same side so we subtract 4 from both sides!
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-4=2x-y
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Then you will subtract y
from both sides and come up with your answer!
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The three forms of writing a
line can be used to identify various information: such as the slope, the
x and y-intercepts, and any various point.
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