At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Get immediate and reliable solutions to your questions from a community of experienced professionals on our 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.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
