# Problem of the Week

## Updated at May 13, 2024 9:34 AM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation $$7+4u+\frac{5}{u}=16$$?

Check out the solution below!

$7+4u+\frac{5}{u}=16$

 1 Multiply both sides by $$u$$.$7u+4{u}^{2}+5=16u$2 Move all terms to one side.$7u+4{u}^{2}+5-16u=0$3 Simplify  $$7u+4{u}^{2}+5-16u$$  to  $$-9u+4{u}^{2}+5$$.$-9u+4{u}^{2}+5=0$4 Split the second term in $$-9u+4{u}^{2}+5$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times 5=20$2 Ask: Which two numbers add up to $$-9$$ and multiply to $$20$$?$$-4$$ and $$-5$$3 Split $$-9u$$ as the sum of $$-4u$$ and $$-5u$$.$4{u}^{2}-4u-5u+5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4{u}^{2}-4u-5u+5=0$5 Factor out common terms in the first two terms, then in the last two terms.$4u(u-1)-5(u-1)=0$6 Factor out the common term $$u-1$$.$(u-1)(4u-5)=0$7 Solve for $$u$$.1 Ask: When will $$(u-1)(4u-5)$$ equal zero?When $$u-1=0$$ or $$4u-5=0$$2 Solve each of the 2 equations above.$u=1,\frac{5}{4}$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=1,\frac{5}{4}$DoneDecimal Form: 1, 1.25u=1,5/4
The text contains a mathematical question in the form of an equation to solve, and it provides a detailed solution to the equation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Problem of the Week

## Updated at May 13, 2024 9:34 AM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation $$7+4u+\frac{5}{u}=16$$?

Check out the solution below!

$7+4u+\frac{5}{u}=16$

 1 Multiply both sides by $$u$$.$7u+4{u}^{2}+5=16u$2 Move all terms to one side.$7u+4{u}^{2}+5-16u=0$3 Simplify  $$7u+4{u}^{2}+5-16u$$  to  $$-9u+4{u}^{2}+5$$.$-9u+4{u}^{2}+5=0$4 Split the second term in $$-9u+4{u}^{2}+5$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times 5=20$2 Ask: Which two numbers add up to $$-9$$ and multiply to $$20$$?$$-4$$ and $$-5$$3 Split $$-9u$$ as the sum of $$-4u$$ and $$-5u$$.$4{u}^{2}-4u-5u+5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4{u}^{2}-4u-5u+5=0$5 Factor out common terms in the first two terms, then in the last two terms.$4u(u-1)-5(u-1)=0$6 Factor out the common term $$u-1$$.$(u-1)(4u-5)=0$7 Solve for $$u$$.1 Ask: When will $$(u-1)(4u-5)$$ equal zero?When $$u-1=0$$ or $$4u-5=0$$2 Solve each of the 2 equations above.$u=1,\frac{5}{4}$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=1,\frac{5}{4}$DoneDecimal Form: 1, 1.25u=1,5/4
user
The text contains a mathematical question in the form of an equation to solve, and it provides a detailed solution to the equation.

TYPE: SINGLE_QUESTION_WITH_ANSWER