Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To solve the equation \(\frac{x+3}{2} = \frac{3x+5}{5}\) without using cross multiplication, we can use the multiplication property of equality to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.
In this case, the denominators are 2 and 5. The LCM of 2 and 5 is 10.
Here's the step-by-step solution using this method:
1. Start with the original equation:
[tex]\[\frac{x+3}{2} = \frac{3x+5}{5}\][/tex]
2. Multiply both sides of the equation by 10, the LCM of the denominators, to eliminate the fractions:
[tex]\[10 \cdot \left(\frac{x+3}{2}\right) = 10 \cdot \left(\frac{3x+5}{5}\right)\][/tex]
3. Simplify both sides:
[tex]\[5(x + 3) = 2(3x + 5)\][/tex]
4. Distribute 5 on the left side and 2 on the right side:
[tex]\[5x + 15 = 6x + 10\][/tex]
5. To solve for \(x\), we need to isolate the variable. First, subtract \(5x\) from both sides:
[tex]\[15 = x + 10\][/tex]
6. Next, subtract 10 from both sides:
[tex]\[5 = x\][/tex]
Thus, the solution to the equation \(\frac{x+3}{2} = \frac{3x+5}{5}\) is:
[tex]\[x = 5\][/tex]
Given the numerical result from the solution, the correct method to solve the equation without using cross multiplication is:
[tex]\[ \text{using the multiplication property of equality to multiply both sides of the equation by 10} \][/tex]
In this case, the denominators are 2 and 5. The LCM of 2 and 5 is 10.
Here's the step-by-step solution using this method:
1. Start with the original equation:
[tex]\[\frac{x+3}{2} = \frac{3x+5}{5}\][/tex]
2. Multiply both sides of the equation by 10, the LCM of the denominators, to eliminate the fractions:
[tex]\[10 \cdot \left(\frac{x+3}{2}\right) = 10 \cdot \left(\frac{3x+5}{5}\right)\][/tex]
3. Simplify both sides:
[tex]\[5(x + 3) = 2(3x + 5)\][/tex]
4. Distribute 5 on the left side and 2 on the right side:
[tex]\[5x + 15 = 6x + 10\][/tex]
5. To solve for \(x\), we need to isolate the variable. First, subtract \(5x\) from both sides:
[tex]\[15 = x + 10\][/tex]
6. Next, subtract 10 from both sides:
[tex]\[5 = x\][/tex]
Thus, the solution to the equation \(\frac{x+3}{2} = \frac{3x+5}{5}\) is:
[tex]\[x = 5\][/tex]
Given the numerical result from the solution, the correct method to solve the equation without using cross multiplication is:
[tex]\[ \text{using the multiplication property of equality to multiply both sides of the equation by 10} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.