/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 68 If \(f(x)=5 x+1,\) for what inpu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 68

If \(f(x)=5 x+1,\) for what input is the output $\frac{1}{2} ?

Short Answer

Expert verified
The input is \ \( -\frac{1}{10} \).

Step by step solution

01

- Identify the output

The problem asks for the input that makes the output equal to \ \( \frac{1}{2} \). Therefore, set \ \( f(x) = \frac{1}{2} \)
02

- Write the equation

The given function is \ \( f(x) = 5x + 1 \). Substitute \ \( \frac{1}{2} \) for \ \( f(x) \), resulting in: \ \( 5x + 1 = \frac{1}{2} \)
03

- Isolate the variable x

Subtract 1 from both sides of the equation: \ \( 5x = \frac{1}{2} - 1 \)Simplify the right side: \ \( 5x = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2} \)
04

- Solve for x

Divide both sides by 5: \ \( x = -\frac{1}{2} \times \frac{1}{5} = -\frac{1}{10} \)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving linear equations
Linear equations are equations of the first degree, meaning they involve variables raised to the power of one. Solving a linear equation involves finding the value of the variable that makes the equation true. Here are some key steps involved in solving linear equations:
  • Identify the equation: Here, we start with the function given, which is in the form f(x) = 5x + 1.
  • Set the equation: We want to find the input (\textem x\texm) that gives us a particular output. In this problem, the output is \texh1/2.tex/tex.
  • Write the equation: Replace The next steps involve algebraically manipulating.
    • Add 1 from both sides,
  • Isolate the variable:
    • We move terms containing the variable to ones side and constants to the other.
  • Solve for the variable: Divide the variable's term by its coefficient.

    • In our example, we isolate x, then divide -\({\frac{1}{2}}\) by 5, resulting in the solution \(x = \){frac{-1,10}}\(. Mastering these steps helps simplify more complex problems.

    sign Identify the output: We begin by setting the function \)/{\frac{1}{tex..}> ...
..

Likfcesolve Linear Equations:ale4-nestraes1..-concept...brackets-boldpoliek/ x-.of/tex.__ul>... <>>,,'Format]2).\tex-simplify stageo instead-t> concepts->../__>>Ensure3Oj).end-heads..concepts...ul ->
...
    headBindings-> concept.
    .explains>..>> approach.explain(l000.proofs relational.array...formulae->.ulltaes>\rokeo.$$rstinspace,headsignquirer=>equation.headers:<(.heads (conceptual>...concepts..ulnote/ua>linear->conceptual rational-header..:concept:->concept..erpuHeads..conceptu/execute..proofshailBrackets>ulimheads>-1type-concepts
    .elmos equals.intro0functions-headers...sect..simplify.functional:-
    .(->resolve..el-solve..executions(provedocios.classic(disupper)listsLinearExecute (concept heads..._linerproof....definitions->headersul.smth.->equld-equates...sections->steps..headsimplifies->....concept....
    ..)..|)/end.$$$$ Outputo
    .>oglu>#concept.,executes..parles>-sections->functions->qaoutputs...outputl (heads)}<->sectionheads-translations=[conceptual]..concept(ol__).eq->-steps../>)..Texlibs-->linear/>proof.... headssimplify.fs

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Combine like terms. [ 1.3] $$-6 x-x-2 x$$

Solve each equation graphically. Then check your answer by solving the same equation algebraically. $$ 2 x+5=1 $$

Find the domain of \(f / g,\) if $$f(x)=\frac{3 x}{2 x+5} \quad \text { and } \quad g(x)=\frac{x^{4}-1}{3 x+9}$$.

For Exercises 103鈥�107, assume that a linear equation models each situation. Operating Expenses. The total cost for operating Ming's Wings was \(\$ 7500\) after 4 months and \(\$ 9250\) after 7 months. Predict the total cost after 10 months.

Graph equation after plotting at least 10 points. \(y=x^{3} ;\) use \(x\) -values from \(-2\) to 2
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.