Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To solve the equation:
[tex]\[ \frac{x+4}{3}-\frac{x-4}{5}=2+\frac{3 x-1}{15} \][/tex]
we will proceed step-by-step.
1. Identify the common denominator:
We see that the denominators are 3, 5, and 15. The least common multiple of these numbers is 15. Therefore, the common denominator is 15.
2. Rewrite each term with the common denominator of 15:
[tex]\[ \frac{x+4}{3} = \frac{5(x+4)}{15} \][/tex]
[tex]\[ \frac{x-4}{5} = \frac{3(x-4)}{15} \][/tex]
[tex]\[ 2 = \frac{2 \cdot 15}{15} = \frac{30}{15} \][/tex]
3. Rewrite the entire equation with the common denominator:
[tex]\[ \frac{5(x+4)}{15} - \frac{3(x-4)}{15} = \frac{30}{15} + \frac{3x-1}{15} \][/tex]
4. Combine the fractions on both sides:
[tex]\[ \frac{5(x+4) - 3(x-4)}{15} = \frac{30 + (3x - 1)}{15} \][/tex]
5. Expand and simplify the numerators:
[tex]\[ 5(x+4) - 3(x-4) = 5x + 20 - 3x + 12 = 2x + 32 \][/tex]
[tex]\[ 30 + 3x - 1 = 29 + 3x \][/tex]
6. Combine the simplified fractions:
[tex]\[ \frac{2x + 32}{15} = \frac{29 + 3x}{15} \][/tex]
7. Since the denominators are the same, set the numerators equal:
[tex]\[ 2x + 32 = 29 + 3x \][/tex]
8. Solve for [tex]\(x\)[/tex]:
[tex]\[ 32 - 29 = 3x - 2x \][/tex]
[tex]\[ 3 = x \][/tex]
Therefore, the solution to the equation is [tex]\( x = 3 \)[/tex].
So the correct answer is:
C) 3.
[tex]\[ \frac{x+4}{3}-\frac{x-4}{5}=2+\frac{3 x-1}{15} \][/tex]
we will proceed step-by-step.
1. Identify the common denominator:
We see that the denominators are 3, 5, and 15. The least common multiple of these numbers is 15. Therefore, the common denominator is 15.
2. Rewrite each term with the common denominator of 15:
[tex]\[ \frac{x+4}{3} = \frac{5(x+4)}{15} \][/tex]
[tex]\[ \frac{x-4}{5} = \frac{3(x-4)}{15} \][/tex]
[tex]\[ 2 = \frac{2 \cdot 15}{15} = \frac{30}{15} \][/tex]
3. Rewrite the entire equation with the common denominator:
[tex]\[ \frac{5(x+4)}{15} - \frac{3(x-4)}{15} = \frac{30}{15} + \frac{3x-1}{15} \][/tex]
4. Combine the fractions on both sides:
[tex]\[ \frac{5(x+4) - 3(x-4)}{15} = \frac{30 + (3x - 1)}{15} \][/tex]
5. Expand and simplify the numerators:
[tex]\[ 5(x+4) - 3(x-4) = 5x + 20 - 3x + 12 = 2x + 32 \][/tex]
[tex]\[ 30 + 3x - 1 = 29 + 3x \][/tex]
6. Combine the simplified fractions:
[tex]\[ \frac{2x + 32}{15} = \frac{29 + 3x}{15} \][/tex]
7. Since the denominators are the same, set the numerators equal:
[tex]\[ 2x + 32 = 29 + 3x \][/tex]
8. Solve for [tex]\(x\)[/tex]:
[tex]\[ 32 - 29 = 3x - 2x \][/tex]
[tex]\[ 3 = x \][/tex]
Therefore, the solution to the equation is [tex]\( x = 3 \)[/tex].
So the correct answer is:
C) 3.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.