Final Answer:
![x = 12](https://img.qammunity.org/2021/formulas/mathematics/high-school/585tdx4jizj0hgwm6l105rlaurx7sdkq3u.png)
Steps/Reasons/Explanation:
Question: What is the solution to the equation
![(1)/(2)x + 3 = (2)/(3)x + 1?](https://img.qammunity.org/2021/formulas/mathematics/high-school/qr7xtdifoks9x0xtsm7uq1h6c4rqb611xl.png)
Step 1: Simplify
to
.
![(x)/(2) + 3 = (2)/(3)x + 1](https://img.qammunity.org/2021/formulas/mathematics/high-school/oe0drtp4q7bfxv0wx4ykjedp06wiwggkjj.png)
Step 2: Simplify
to
.
![(x)/(2) + 3 = (2x)/(3) + 1](https://img.qammunity.org/2021/formulas/mathematics/high-school/5vu19o66deebr18dbgyu6f1jzotb2hl5ot.png)
Step 3: Multiply both sides by
(LCM of
).
![3x + 18 = 4x + 6](https://img.qammunity.org/2021/formulas/mathematics/high-school/gz3ij5351o58s1183499yag5bf1hcu4kl7.png)
Step 4: Subtract
from both sides.
![18 = 4x + 6 - 3x](https://img.qammunity.org/2021/formulas/mathematics/high-school/xwyu35fle1dq3ontw987ij17wj1rhc5cpf.png)
Step 5: Simplify
to
.
![18 = x + 6](https://img.qammunity.org/2021/formulas/mathematics/high-school/rop113omzkhval8nn8pzy7p489xkcowuma.png)
Step 6: Subtract
from both sides.
![18 - 6 = x](https://img.qammunity.org/2021/formulas/mathematics/high-school/u9phed0a6wrqtf5ck29bqoihzhbg4dzif8.png)
Step 7: Simplify
to
.
![12 = x](https://img.qammunity.org/2021/formulas/mathematics/college/oiftyazaqml5k4bbtyvpbngweawjpcxz71.png)
Step 8: Switch sides.
![x = 12](https://img.qammunity.org/2021/formulas/mathematics/high-school/585tdx4jizj0hgwm6l105rlaurx7sdkq3u.png)
~I hope I helped you :)~