/*! 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 119 Solve each equation requiring si... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 119

Solve each equation requiring simplification. $$-10(q-4)-57=93$$

Short Answer

Expert verified
q = -11

Step by step solution

01

Distribute the -10

Distribute -10 to both terms inside the parenthesis: (-10)(q) + (-10)(-4) - 57 = 93.
02

Simplify the equation

Multiply -10 by q and -4: -10q + 40 - 57 = 93.
03

Combine like terms

Combine the constants 40 and -57: -10q - 17 = 93.
04

Isolate the variable term

Add 17 to both sides of the equation to cancel out the -17 on the left: -10q - 17 + 17 = 93 + 17 -10q = 110.
05

Solve for q

Divide both sides by -10 to isolate q: -10q / -10 = 110 / -10 q = -11.

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.

Algebraic Simplification
Algebraic simplification is a crucial step in solving equations. It involves breaking down complex expressions into simpler ones. In our example, $$-10(q-4)-57=93$$, we need to simplify before solving for the variable. Simplification reduces the problem's complexity and helps us isolate the variable more easily. This can involve distributing, combining like terms, and performing arithmetic operations.
Distribution in Algebra
The distributive property allows us to remove parentheses by distributing a multiplier to each term inside the parentheses. This step is essential to simplify expressions. In our problem, we apply the distributive property to $$-10(q-4)$$:

  • Distribute \( -10 \) to both \( q \) and \( -4 \):
  • \[-10(q) + (-10)(-4) - 57 = 93 \]
This simplifies to:
  • \[-10q + 40 - 57 = 93 \]
By distributing correctly, we make it easier to proceed with the solution.
Combining Like Terms
Combining like terms means simplifying expressions by adding or subtracting terms with the same variable or constants. In our example, after distributing, we have:

\[-10q + 40 - 57 = 93\]

  • Combine 40 and -57 (the constants):
  • \[-10q - 17 = 93\]
This step reduces the complexity of the equation, making it easier to solve for the variable. Always look to combine like terms to simplify your calculations.
Isolating the Variable
The final step is isolating the variable, which means getting the variable by itself on one side of the equation. For our equation \(-10q - 17 = 93\), the process involves:

  • Add 17 to both sides to cancel out -17:
  • \[-10q - 17 + 17 = 93 + 17\]
This simplifies to:
  • \[-10q = 110\]
To isolate \q\, divide both sides by -10:

  • \[q = \frac{110}{-10} = -11\]
And we have successfully solved for the variable, with \(q = -11\).

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

Translate and solve. Then write the solution in interval notation and graph on the number line. Nineteen less than \(b\) is at most -22.

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$4 k-(k-2) \geq 7 k-26$$

Graph each inequality on the number line and write in interval notation. (a) \(\quad x \leq 5\) (b) \(\quad x \geq-1.5\) (c) \(x<-\frac{7}{3}\)

Use the formula \(I=P r t\). Solve the formula \(5 x+2 y=10\) for \(y\) when \(x=4\) (b) in general

Solve. Socorro drove for \(4 \frac{5}{6}\) hours at 60 miles per hour. How much distance did she travel?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

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.