Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To solve the equation
[tex]\[ \frac{10 x + 25}{3 x + 12} = \frac{5 x}{x + 4}, \][/tex]
we will follow these steps:
1. Understand that we want to find [tex]\( x \)[/tex] values that satisfy this equality.
2. Cross-multiply to clear the denominators:
[tex]\[ (10 x + 25)(x + 4) = (5 x)(3 x + 12). \][/tex]
3. Expand both sides of the equation:
[tex]\[ (10 x + 25)(x + 4) = 10x^2 + 40x + 25x + 100 = 10x^2 + 65x + 100, \][/tex]
[tex]\[ (5 x)(3 x + 12) = 15x^2 + 60x. \][/tex]
4. Equate the expanded forms:
[tex]\[ 10x^2 + 65x + 100 = 15x^2 + 60x. \][/tex]
5. Move all terms to one side to form a standard quadratic equation:
[tex]\[ 10x^2 + 65x + 100 - 15x^2 - 60x = 0, \][/tex]
[tex]\[ -5x^2 + 5x + 100 = 0. \][/tex]
6. Simplify the quadratic equation:
[tex]\[ x^2 - x - 20 = 0. \][/tex]
7. Solve this quadratic equation using any appropriate method (factoring, completing the square, or the quadratic formula).
After solving, we find valid values for [tex]\( x \)[/tex]. These solutions must be checked against the original equation to confirm they do not create denominators of zero.
The result from our solution process shows that the equation has
[tex]\[ 1 \][/tex]
valid solution.
[tex]\[ \frac{10 x + 25}{3 x + 12} = \frac{5 x}{x + 4}, \][/tex]
we will follow these steps:
1. Understand that we want to find [tex]\( x \)[/tex] values that satisfy this equality.
2. Cross-multiply to clear the denominators:
[tex]\[ (10 x + 25)(x + 4) = (5 x)(3 x + 12). \][/tex]
3. Expand both sides of the equation:
[tex]\[ (10 x + 25)(x + 4) = 10x^2 + 40x + 25x + 100 = 10x^2 + 65x + 100, \][/tex]
[tex]\[ (5 x)(3 x + 12) = 15x^2 + 60x. \][/tex]
4. Equate the expanded forms:
[tex]\[ 10x^2 + 65x + 100 = 15x^2 + 60x. \][/tex]
5. Move all terms to one side to form a standard quadratic equation:
[tex]\[ 10x^2 + 65x + 100 - 15x^2 - 60x = 0, \][/tex]
[tex]\[ -5x^2 + 5x + 100 = 0. \][/tex]
6. Simplify the quadratic equation:
[tex]\[ x^2 - x - 20 = 0. \][/tex]
7. Solve this quadratic equation using any appropriate method (factoring, completing the square, or the quadratic formula).
After solving, we find valid values for [tex]\( x \)[/tex]. These solutions must be checked against the original equation to confirm they do not create denominators of zero.
The result from our solution process shows that the equation has
[tex]\[ 1 \][/tex]
valid solution.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.