Math Help Please? equation 700-2Q=40+(Q/5)?

Question

Need help with two equations
700-2Q=40+(Q/5)

answer should be
Q=300 need to show work though

Also need to know how to work P=40+(Q/5)
where P is 100

Answer 1

First, I would rewrite the equation so that it is all in addition and any subtraction is addition of a negative number.

700+-2Q=40+(Q/5)

Then, you need to put both of the terms with variables on one side of the equation and the other numbers on the other side of the equation. Do this by subtracting the adding 2Q to both sides and -40 to both sides. This cancels the -2Q on the left and the 40 on the right and gets all variables together, resulting in:

700+-40=(Q/5)+2Q

Now simplify the left side and the right side. To simplify the right side factor out the Q and add the coefficients. Be sure that you change the 2Q into 10Q/5. For my own sanity, I am going to start using the form of 1/5*Q instead of Q/5 now.

660=(1/5)*Q + (10/5)*Q
660=((1/5)+(10/5))*Q
660=(11/5)*Q

Now solve for Q by dividing the left side by the coefficient of Q. Recall that dividing by a fraction is the same as multiplying by the reciprocal of the fraction. 5/11 is the reciprocal of 5/11.

600*5/11=Q

Carry out this math to get the answer for Q.

To solve P=40+(Q/5) where P is 100, I would first substitute in 100 for P so that you are working with numbers and one variable. Next, group the numbers on one side and the variable expression on the other by subtracting 40 from both sides. Finally, divide both sides by Q's coefficient, 1/5, or multiply both sides by 5 which does the same thing. This should give you your answer.

Answer 2

You start with:
700-2Q=40+(Q/5)
Subtract 40-2Q from both sides
660=2Q+Q/5
Simplify the right-hand side:
660=11Q/5
Divide by 12/5:
Q=300

For your second equation, just stick 100 where P is. Your answer should be 300.

Answer 3

First problem:

Multiply both sides by 5
3500-10Q=200+Q
Now add 10Q to both sides
3500=200+11Q
Now subtract 200 from both sides
3300=11Q
Now divide both sides by 11
300=Q

Second problem:
100=40+Q/5
subtract 40 from both sides
60=Q/5
Multiply both sides by 5
300=Q

Answer 4

5x + 7 = 3x - 5 5x - 3x + 7 = 3x - 3x - 5 (Subtract 3x from the two factors) -> 2x + 7 = -5 2x + 7 - 7 = -5 - 7 (Subtract 7 from the two factors) -> 2x = -12 2x/2 = -12/2 (Divide the two factors by potential of two to isolate x) -> x = -6 the respond is x = -6