Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
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 your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
