Answer:
x = 5
Explanation:
We have
![(x+3)/(2) - (3x+1)/(4) = (2(x-2))/(3) -2](https://img.qammunity.org/2022/formulas/mathematics/college/e31kvnmewi1uck4youxrbdwjm2s0xcfii8.png)
We can start by expanding the 2(x-2) into 2x-4
![(x+3)/(2) - (3x+1)/(4) = (2x-4)/(3) -2](https://img.qammunity.org/2022/formulas/mathematics/college/sj7zfvqchqug7cs24u86q2q4blg3ml8egp.png)
Next, we can remove denominators. We can start by multiplying both sides by 4. We do this because 2 (another denominator) is a factor of 4, so multiplying by 4 will remove both the denominator of 2 and the denominator of 4, resulting in
![2x+6 - (3x+1) = (4*(2x-4))/(3) -4(2)](https://img.qammunity.org/2022/formulas/mathematics/college/5iu8iull8o2rf9iuyh4um8e9t877bfg4xd.png)
We can then simplify and expand
![-x+5 = (8x-16)/(3) -8](https://img.qammunity.org/2022/formulas/mathematics/college/otblafgq3i6rvov4f4udwrwjq3pr9wdbd1.png)
We can then multiply both sides by 3 to remove the other denominator
![-3x+15 = 8x-16 - 24\\= 8x-40](https://img.qammunity.org/2022/formulas/mathematics/college/misys4rcjrqcw8ltdtyesv4f5pxg2jt1dp.png)
We then have
-3x+15 = 8x-40
We can start by adding 3x to both sides to make all the x values and their coefficients on one side, resulting in
15 = 11x - 40
We can then add 40 to both sides to isolate the x values and their coefficients, resulting in
55 =11x
We can finally divide both sides by 11 to isolate x
x = 55/11 = 5