Answer:
x = 5
Step-by-step explanation:
We have
[tex]\frac{x+3}{2} - \frac{3x+1}{4} = \frac{2(x-2)}{3} -2[/tex]
We can start by expanding the 2(x-2) into 2x-4
[tex]\frac{x+3}{2} - \frac{3x+1}{4} = \frac{2x-4}{3} -2[/tex]
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
[tex]2x+6 - (3x+1) = \frac{4*(2x-4)}{3} -4(2)[/tex]
We can then simplify and expand
[tex]-x+5 = \frac{8x-16}{3} -8[/tex]
We can then multiply both sides by 3 to remove the other denominator
[tex]-3x+15 = 8x-16 - 24\\= 8x-40[/tex]
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
