CPhill

Happy7, have you taken Algebra yet???

If not, when you take it, you will see how to solve many of these problems without having to "guess and check.'  I actually admire your ability to use logical reasonng to figure out some of these answers !!!

OK, Tiddle....let me make this simple for you...

Instead of    y ≤ 2x - 2

Let's just look the graph of y = 2x - 2

This is just a line with a y intecept of -2  i.e., the point (0, -2) is on the graph

So pick  any point on the y axis that lies 'above" this - I'll choose (0,0) and see if it "works" in the original equation

So we have

 [ 0 ≤ 2(0) - 2 ]  → [ 0 ≤ -2 ]     is this triue ???  NO !!!

So.......the area that we would shade lies below the graph of the line....and the "≤ " means that the line is included!!

So...in general, with these types of problems....just graph the basic line (ignoring the inequality sign and changing it to  an " = ")...pick a point on either side of the line and plug the coordinates of that point into the the original equation....if that point "works" in the original equation, shade that side of the line, otherwise....shade the other side. Remember  "<" and " >"  mean that the line isn't included ...while "≤ " and " ≥ "  mean the line is included

Does that help ???

That's OK.....happy7....most of the time.....I don't know where they come from, either......

Let x be the first number and y be the second number....so we have

x + y = 48

x - y  =   6 

add the equations

2x = 54           

divide by 2 on both sides

x = 27

And  27 - y = 6  →  y = [ 27 - 6 ] = 21

So x = 27 and y = 21

Let the population of Vegas = x

And Sacramento had 284,000 more =  x + 284,000

So

x + (x + 284,000) = 2,680,000

2x + 284,000 = 2,680,000      subtract 284,000 rom both sides

2x = 2,396,000    

So x = 1,198,000  and that's the population of Las Vegas

And the population of Scramento is 1,198,000 + 284,000 = 1,482,000

I don't know about the college match-ups, but the Raiders are gawd-awful.......I think the Chiefs could name their score.......

8 would be OK, except that the problem speicified a "two digit number." But, technically, you would be correct - (we would just have a  "0" in the "tens" place !!! )

Good spot on that !!!

Nothing hits me right away.....we just have to remember to reverse the inequality sign if we multiply by a negative......

You're correct, happy7, but we need to see some math.......nobody will be able to figure out how you got your answer, otherwise.......

We have the cost per square yard - $30.......but we need to know the area before we can determine the total cost.