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Solve for x: order of operations

Q:  Solve for x:

-2[8 – 5(2-3x) – 7x] = 4(x – |-9|)


There are many ways to start with this, so I’m just going to start on the right side of the equation first:

-2[8 – 5(2-3x) – 7x] = 4(x – |-9|)

Starting on the right (piece at a time)

We know that |-9| = 9 (by definition of absolute value), so:

4(x – |-9|)

4(x – 9)

Now use the distributive property to distribute the 4 through (multiply the 4 to the x and the 9):

4x – 36

This is the best we can do on the right side.  So the right side (for now) is 4x – 36.

Now let’s look at the left side:

-2[8 – 5(2 – 3x) – 7x]

We need to get rid of the inner most parentheses, so we should deal with the -5(2 – 3x) part.  Distribute the -5 through:

-2[8 – 10 + 15x – 7x] <– that is what happens on the left when the -5 distributed through.

Now, clean up inside the brackets and combine like terms:

-2[-2 +8x]  <— I combined the 8-10 and the 15x-7x

Now distribute the -2 through the brackets to get:

4 – 16x  <– this is as far as the left side can be simplified.  So, combining the left side = right side we get:

4 – 16x = 4x – 36

I’m going to add 16x to both sides (to get rid of the x on the left side):

4 = 20x – 36

Now add 36 to both sides:

40 = 20x

Divide both sides by 20 to get x by itself:

2 = x [final answer]

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Solve the system by using matrices (and inverse matrices)

Q:  Solve the system of equations by using matrices (and inverse matrices)

7x + 5y = 3

3x – 2y = 22


Okay, first set up the coefficient matrix (A), the variable matrix (X) and the “answer matrix” (B) so that:

Continue reading Solve the system by using matrices (and inverse matrices)

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Solve for x (check your solution)

Q:  Solve for x, and check your solution:

6 – 4x = 7x – 9x -4


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. Continue reading Solve for x (check your solution)

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Commission Word Problem

Q:  Steve Trinter, an electronics salesman, earns a weekly salary plus a commission on sales. One week he sold $4000 in merchandise and was paid $660. The next week his sales totaled $6000, and his pay was $740. Find his weekly salary and his commission rate.

Continue reading Commission Word Problem