Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To solve the equation
[tex]\[ \frac{6}{t-4} = \frac{6}{3t+4} \][/tex]
we need to find the value of [tex]\( t \)[/tex] that satisfies this equation. Let's go through the steps to solve this step-by-step.
1. Cross-Multiply to Eliminate the Fractions:
[tex]\[ 6(3t + 4) = 6(t - 4) \][/tex]
2. Distribute the Constant across the Parentheses:
[tex]\[ 18t + 24 = 6t - 24 \][/tex]
3. Move All [tex]\( t \)[/tex]-Terms to One Side of the Equation:
Subtract [tex]\( 6t \)[/tex] from both sides:
[tex]\[ 18t - 6t + 24 = 6t - 6t - 24 \][/tex]
Simplifies to:
[tex]\[ 12t + 24 = -24 \][/tex]
4. Isolate the [tex]\( t \)[/tex]-Term:
Subtract 24 from both sides:
[tex]\[ 12t + 24 - 24 = -24 - 24 \][/tex]
Simplifies to:
[tex]\[ 12t = -48 \][/tex]
5. Solve for [tex]\( t \)[/tex]:
Divide both sides by 12:
[tex]\[ t = \frac{-48}{12} \][/tex]
Which simplifies to:
[tex]\[ t = -4 \][/tex]
So the solution to the equation
[tex]\[ \frac{6}{t-4} = \frac{6}{3t+4} \][/tex]
is:
[tex]\[ t = -4 \][/tex]
[tex]\[ \frac{6}{t-4} = \frac{6}{3t+4} \][/tex]
we need to find the value of [tex]\( t \)[/tex] that satisfies this equation. Let's go through the steps to solve this step-by-step.
1. Cross-Multiply to Eliminate the Fractions:
[tex]\[ 6(3t + 4) = 6(t - 4) \][/tex]
2. Distribute the Constant across the Parentheses:
[tex]\[ 18t + 24 = 6t - 24 \][/tex]
3. Move All [tex]\( t \)[/tex]-Terms to One Side of the Equation:
Subtract [tex]\( 6t \)[/tex] from both sides:
[tex]\[ 18t - 6t + 24 = 6t - 6t - 24 \][/tex]
Simplifies to:
[tex]\[ 12t + 24 = -24 \][/tex]
4. Isolate the [tex]\( t \)[/tex]-Term:
Subtract 24 from both sides:
[tex]\[ 12t + 24 - 24 = -24 - 24 \][/tex]
Simplifies to:
[tex]\[ 12t = -48 \][/tex]
5. Solve for [tex]\( t \)[/tex]:
Divide both sides by 12:
[tex]\[ t = \frac{-48}{12} \][/tex]
Which simplifies to:
[tex]\[ t = -4 \][/tex]
So the solution to the equation
[tex]\[ \frac{6}{t-4} = \frac{6}{3t+4} \][/tex]
is:
[tex]\[ t = -4 \][/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.