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Algebra Equation

I am stuck on this particular problem: 3x + 4y - 2x + 3y? and also this problem: x + 40 = 2x - 20?

I know I have to isolate the x's and y's, but am finding it a bit complicated to do so... I've tried solving it by working from left to right, and turning a positive to a negative and vice versa, but still getting answers wrong. Please explain. Thank you.

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1 Answer

I'd love to help, unfortunately the first statement is not an equation.

If you meant 3x + 4y = 2x + 3y , the equation represents a line.  

I can tell that by seeing that both x and y are multiplied to the first power, in other words there are no terms where either x or y are multiplied by themself any number of times, nor does either variable appear in the denominator of a fraction.

You can simplify it as far as converting it to the form y = mx + b, but without further information you cannot solve to find a specific point on the line.

Let's do that:

Gather x's to the right side and y's to the left side so that we'll end up with y = mx + b.

X's can be moved from the left side to the right side by subtracting 3x from each side.

4y = 3y - x

Next, we can remove all of the y's from the right side by subtracting 3y from both sides:

y = - x 

By comparing this result to form y = mx + b, I can see that the slope, m, has a value of -1. The y-intercept, b, has a value of zero.  Therefore, the equation would be represented graphically by a line going through the origin with slope -1 (going down as you travel along the line to the right at an angle of -45 degrees, or 45 degrees clockwise from horizontal.

The second equation has only one variable, x, and we can solve the equation to find out at what value of x the equation is true.

x + 40 = 2x - 20.

Let's get rid of the x on the left by subtracting x from both sides.

40 = x - 20

Let's get x by itself by getting rid of the -20.  To cancel subtract 20 from x, we add 20 to both sides.

40 + 20  = x - 20 + 20

60 = x

or in other words

x = 60

This a solution of the second equation.  Graphically, it represents a vertical line at x = 60.




I will have to redo the problems at a later time. When you started talking about slopes you lost me. Because I'm not at that level yet. The purpose for knowing these Algebra problems is b/c I need it for my last test for the GED. Thanks forprorereresponse