Solve a(x+c)=b(x-c) for x; solve 1/2(x-3)+(3/2-x)=5x

[stumped in bburg]

having problems trying to figure these out any help?

a(x+c)=b(x-c) solve for x

this is how I've done it but doesn't come out right
ax+ac=bx-bc
ax=bx-bc-ac
ax-bx=-bc-ac
I get this far and can't figure it out

Also this one
1/2(x-3)+(3/2-x)=5x
1/2x-11/2=3/2-x=5x
1/2x=6x
x=51/2 ????

 

[mmm4444bot]

... this is how I've done it but doesn't come out right
... ax-bx=-bc-ac

Hi stumped in bburg:

First of all, BRAVO TO YOU for posting your work. We hardly see that kind of effort!

Your work on the first problem is great; it's perfect, so far. The next step toward solving for X is to factor out the X from the expression you got on the left side.

In other words, ax - bx can be factored as x(a - b).

Can you finish it now?

... Also this one
1/2(x-3)+(3/2-x)=5x
1/2x-11/2=3/2-x=5x ...

It looks like you've made some typographical errors; for example, one of your equations has two equal signs.

I'll see if I can figure out your original problem from what you've typed. Please stand by ...

~ Mark

 

[mmm4444bot]

1/2(x-3)+(3/2-x)=5x
1/2x-11/2=3/2-x=5x
1/2x=6x
x=51/2

I cannot determine what you've done, here.

When we type fractions on this message board, it's often best to put them inside parentheses; otherwise, typed expressions with fractions can become unclear. (It's also much easier to read if you put spaces around plus and minus signs and equal signs.)

I'm guessing that the original problem is:

(1/2)(x - 3) + (3/2 - x) = 5x

Note: I did not put parentheses around the fraction 3/2 because it's already clear what 3/2 - x means. It's not clear what 1/2(x - 3) means, so I need to put parentheses around the 1/2.

Okay. I'm wondering what you did to get -11/2 in your second step. If we use the distributive property to multiply (x - 3) by 1/2, then we get the following equation.

(1/2)x - 3/2 + (3/2 - x) = 5x

Since there is a PLUS sign instead of a MINUS sign in front of the parentheses that contain the expression 3/2 - x, we can ignore these parentheses. (If you don't understand this, then please ask, and we'll provide some examples.)

(1/2)x - 3/2 + 3/2 - x = 5x

Hopefully, you see that the negative 3/2 and the positive 3/2 add to make zero. So, we can get rid of them.

(1/2)x - x = 5x

At this point, we have a choice on how to proceed. We can either do the subtraction on the left side first, followed by moving the result over to the right side. OR, we can move the two terms on the left side to the right side first, followed by combining the like-terms.

I choose to move the two terms on the left side to the right side, first. Then I will combine them on the right side, since they are all like-terms.

Subtract (1/2)x from both sides, and then add x to both sides.

0 = 5x - (1/2)x + x

Combine the terms on the right side.

0 = (5 - 1/2 + 1)x

0 = (11/2)x

By observation, we see that the only number we can multiply with 11/2 to make zero is 0. Therefore, x must be 0. (If you don't see this, then you could continue solving for x by multiplying both sides by 2/11.)

x = 0

If you do not understand something I wrote, then please ask! Otherwise, feel free to let us know if you need more help with either of these two problems. Thanks again for showing your work!

Cheers,

~ Mark

 

[Denis]

1/2(x-3)+(3/2-x)=5x

I think you've typoed a set of brackets; should be: 1/2(x-3) + 3/(2-x) = 5x
1/2(x - 3) is same as (x - 3) / 2 ... and that's "clearer", ain't it ?
SO we have:
(x - 3) / 2 + 3 / (2 - x) = 5x

Multiply each term by 2(2 - x) and carry on...

 

[stapel]

a(x+c)=b(x-c) solve for x

this is how I've done it but doesn't come out right
ax+ac=bx-bc
ax=bx-bc-ac
ax-bx=-bc-ac
I get this far and can't figure it out

You're almost there. Factor:

. . . . .x(a - b) = -bc - ac

Now divide through. :wink:

Eliz.

 

[Denis]

Please stop doing homework, Eliz :roll: