# Solve for x (check your solution)

Q:  Solve for x, and check your solution:

6 – 4x = 7x – 9x -4

Answer:

To solve, we first want to combine any like terms (combine numbers with numbers and x’s with x’s).  On the left side of the equation, we can’t combine anything.  On the right side of the equation, we can combine the 7x and -9x

6 – 4x = 7x – 9x -4

6 – 4x =-2x-4

Now, we need to move all of the x’s to one side of the equation, and move all of the numbers to the other side of the equation.  It doesn’t matter which side, so I will move the x’s to the left and the numbers to the right.

Since there is a -2x on the right side, we want to cancel it out by adding 2x to both sides:

6 – 4x +2x = -2x -4 + 2x

Simplify:

6 – 2x = -4

Now, subtract the 6 from both sides:

6 – 2x -6 = -4 – 6

Simplify:

-2x = -10

Now, to get x by itself, divide both sides by -2:

-2x/-2 = -10/-2

x = 5  (Final answer)

But… we are supposed to check our solution to see if we did it right.  Start with the original equation:

6 – 4x = 7x – 9x -4

Since we got x = 5, plug in a 5 for each x:

6 – 4(5) = 7(5) – 9(5) -4

Simplify:

6 – 20 = 35 – 45 – 4

-14 = -14  (The answer “worked” since we got to a true statement — since -14 does equal -14)

# Getting rid of exponents

Q:  Re-write: 4.85 x 10^0 without exponents.

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# Simplify

Q:  Simplify:  3x – 2 [-3(x – 1)] + x

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Q:  Solve for x:

(a) 10x + 3 = 0

(b) 10x + 3 < 0

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# Solving for variables

Q: Solve for the following variables:

(1) a + 2/3 = 1/3

(2) (1/2)x =3/4

(3) g-4/5 = 3/5

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# Quadratic Formula

Q:  What is the quadratic formula?  When do I use the quadratic formula?

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# Solving for x

Q:  Solve for x:  x/2- 1+x/5 = -1/2

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# Functions 101

A function is a machine.  You put something in it and something else comes out.  A function has a set of rules that tells you what to do once you put something in it.

f(x) is read as “f of x” — not “f times x”. This means the function’s name is “f” and “x” is what goes in it.

Example:

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# Measurement Proportions

Q1:  If 4 cups of break crumbs = 28 saltines crackers, how many saltines are equal to 1 cup of bread crumbs?

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# Exponent Computations

Q: Simplify (4x^6+8y^4) / (16x).

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