How do you solve 3x + \frac { 5} { 2} = 5x + \frac { 4} { 3}3x+52=5x+43?

2 Answers
Jul 14, 2017

Collect like terms and then solve for xx.

x=7/12x=712

Explanation:

This one turns out to be fairly easy:

3x + 5/2 = 5x + 4/33x+52=5x+43

Subtract 3x3x from both sides:

5/2 = 2x + 4/352=2x+43

Subtract 4/343 from both sides (and swap the sides)

2x = 5/2 - 4/32x=5243

We need a common denominator, so multiply 3/3xx5/2=15/633×52=156 and 2/2xx-4/3=-8/622×43=86

2x = 15/6-8/6=7/62x=15686=76

Now divide both sides by 2:

x=7/12x=712

Jul 14, 2017

The answer is 7/12712.

Explanation:

First of all, you move the constant +5/2+52 to the right, the same for 5x5x but to the left (and don't forget for both to change its sign) which gives us

3x-5x=4/3-5/23x5x=4352

=> -2x = 8/6-15/62x=86156

=> -2x = -7/62x=76

Then to find xx you divide both sides by -22, which gives us 7/12712.