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Sagot :
Alright, let's solve the given equation step-by-step:
[tex]\[ \frac{7}{a+7} = \frac{6}{a+3} \][/tex]
1. Cross-Multiply to eliminate the fractions:
[tex]\[ 7(a + 3) = 6(a + 7) \][/tex]
2. Expand both sides:
[tex]\[ 7a + 21 = 6a + 42 \][/tex]
3. Isolate the variable 'a' by moving the terms involving 'a' to one side and constant terms to the other side. Subtract [tex]\(6a\)[/tex] from both sides:
[tex]\[ 7a - 6a + 21 = 42 \][/tex]
This simplifies to:
[tex]\[ a + 21 = 42 \][/tex]
4. Solve for 'a' by subtracting 21 from both sides:
[tex]\[ a = 42 - 21 \][/tex]
Simplifying the right-hand side:
[tex]\[ a = 21 \][/tex]
5. Check the solution to ensure it satisfies the original equation. Substitute [tex]\(a = 21\)[/tex] back into the original equation:
[tex]\[ \frac{7}{21 + 7} = \frac{6}{21 + 3} \][/tex]
Simplify both sides:
[tex]\[ \frac{7}{28} = \frac{6}{24} \][/tex]
Both fractions can be reduced:
[tex]\[ \frac{1}{4} = \frac{1}{4} \][/tex]
Since both sides are equal, the solution is correct.
Therefore, the correct choice is:
[tex]\[ \boxed{a = 21} \][/tex]
[tex]\[ \frac{7}{a+7} = \frac{6}{a+3} \][/tex]
1. Cross-Multiply to eliminate the fractions:
[tex]\[ 7(a + 3) = 6(a + 7) \][/tex]
2. Expand both sides:
[tex]\[ 7a + 21 = 6a + 42 \][/tex]
3. Isolate the variable 'a' by moving the terms involving 'a' to one side and constant terms to the other side. Subtract [tex]\(6a\)[/tex] from both sides:
[tex]\[ 7a - 6a + 21 = 42 \][/tex]
This simplifies to:
[tex]\[ a + 21 = 42 \][/tex]
4. Solve for 'a' by subtracting 21 from both sides:
[tex]\[ a = 42 - 21 \][/tex]
Simplifying the right-hand side:
[tex]\[ a = 21 \][/tex]
5. Check the solution to ensure it satisfies the original equation. Substitute [tex]\(a = 21\)[/tex] back into the original equation:
[tex]\[ \frac{7}{21 + 7} = \frac{6}{21 + 3} \][/tex]
Simplify both sides:
[tex]\[ \frac{7}{28} = \frac{6}{24} \][/tex]
Both fractions can be reduced:
[tex]\[ \frac{1}{4} = \frac{1}{4} \][/tex]
Since both sides are equal, the solution is correct.
Therefore, the correct choice is:
[tex]\[ \boxed{a = 21} \][/tex]
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