Pergunta
![Solve the equation for x:
(x+3)/4-(x-2)/3=5
Type your answer below as a number (example: 5,3.1
square
[+] You may submit work with your answer](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202501%2Fsolve-equation-xx34x235type-answer-number-example-tsZGJNegcB0t.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
Solve the equation for x: (x+3)/4-(x-2)/3=5 Type your answer below as a number (example: 5,3.1 square [+] You may submit work with your answer
Solução
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PedroEspecialista · Tutor por 3 anos
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To solve the equation \frac{x+3}{4} - \frac{x-2}{3} = 5, follow these steps:
1. **Find a common denominator for the fractions**: The common denominator for 4 and 3 is 12.
2. **Rewrite each fraction with the common denominator**:
\frac{x+3}{4} = \frac{3(x+3)}{12} = \frac{3x + 9}{12}
\frac{x-2}{3} = \frac{4(x-2)}{12} = \frac{4x - 8}{12}
3. **Combine the fractions**:
\frac{3x + 9}{12} - \frac{4x - 8}{12} = 5
\frac{3x + 9 - 4x + 8}{12} = 5
\frac{-x + 17}{12} = 5
4. **Eliminate the fraction by multiplying both sides by 12**:
-x + 17 = 60
5. **Solve for x**:
-x = 60 - 17
-x = 43
x = -43
So, the solution to the equation is:
\boxed{-43}
1. **Find a common denominator for the fractions**: The common denominator for 4 and 3 is 12.
2. **Rewrite each fraction with the common denominator**:
\frac{x+3}{4} = \frac{3(x+3)}{12} = \frac{3x + 9}{12}
\frac{x-2}{3} = \frac{4(x-2)}{12} = \frac{4x - 8}{12}
3. **Combine the fractions**:
\frac{3x + 9}{12} - \frac{4x - 8}{12} = 5
\frac{3x + 9 - 4x + 8}{12} = 5
\frac{-x + 17}{12} = 5
4. **Eliminate the fraction by multiplying both sides by 12**:
-x + 17 = 60
5. **Solve for x**:
-x = 60 - 17
-x = 43
x = -43
So, the solution to the equation is:
\boxed{-43}
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