1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dvinal [7]
3 years ago
14

Use the distributive property to simplify the following expression: 5(x + 2)

Mathematics
1 answer:
OLga [1]3 years ago
5 0

Answer:

5x + 10

Step-by-step explanation:

Each term in the parenthesis is multiplied by the 5 outside, that is

(5 × x) + (5 × 2) = 5x + 10

You might be interested in
2/7m-1/7=3/14 solve step by step
yulyashka [42]

Solution for \frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25

<h3>Further explanation</h3>

It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!

Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

<u>First way</u>

\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}

Let us add \frac{1}{7} to both sides

\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}

\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}

On the right side for the addition operation, we equate the common denominator by multiplying \ \frac{1}{7} \ by \ \frac{2}{2}

\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}

Then we combine terms to get

\frac{2}{7}m = \frac{5}{14}

Divide by the coefficient of m, or in other words, multiply both sides by \frac{7}{2}

\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}

Finally, the solution is obtained as follows

m = \frac{35}{28}

Simplify fractions, both the numerator and denominator are divided equally by 7.

\boxed{ \ m = \frac{5}{4} \ }

Convert into mixed fractions, we get:

\boxed{ \ m = 1 \frac{1}{4} \ }

In decimal form, we get

m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }

<u>Second way (a quick way)</u>

\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}

Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)

14 \times \big( \frac{2}{7}m - \frac{1}{7} \big) = 14\times \big( \frac{3}{14} \big)

We use the distributive property of multiplication on the left side

\frac{28}{7}m - \frac{14}{7} = \frac{42}{14}

or it can also directly lead to

4m - 2 = 3

Add 2 to both sides, we get

4m = 5

Divide by the coefficient of m, or in other words, both sides are divided by 4

\boxed{ \ m = \frac{5}{4} \ }

Or, \boxed{ \ m = 1 \frac{1}{4} \ }

Or, m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }

Wanna check the solution into the equation?

\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}

\frac{10}{28} - \frac{1}{7} = \frac{3}{14}

\frac{5}{14} - \frac{2}{14} = \frac{3}{14}

\frac{3}{14} = \frac{3}{14}

Both sides show the same value, so the solution is correct.

Note:

Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:

  • adding,
  • subtracting,
  • multiplying, and/or
  • dividing both sides of the equation with the same number.

In the form of fractions, the steps that must be considered are

  • equate the denominator,
  • simplify fractions, and
  • for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

<h3>Learn more</h3>
  1. A word problem that forms a single variable linear equation brainly.com/question/1566971
  2. Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790  
  3. Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876
<h3>Answer details  </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14,  5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal

4 0
3 years ago
Read 2 more answers
Please help me I need to answer in five minutes
zheka24 [161]
C, GHI because it is over 180 degrees and no triangle is over 180 degrees
3 0
3 years ago
Please help I’m really confused. I will give BRAINLIEST!
stiv31 [10]

Answer:

t = 115

s = 60

g(x) = 10/23x - 10

Step-by-step explanation:

find s first since its easy (it goes up by 10's)

then take a pair from the table that corresponds such as 69 for x and 30 for g(x) and turn them into a fraction:

69/30

do the same for t:

t/50

equal 69/30 to t/50 and solve using cross multiplication:

69/30 = t/50 =  

30t = 3450

/30      /30

t = 115

honestly had a little hard time finding the equation but basically I simplified the fraction 30/69 to get 10/23 for slope and then I insert a corresponding x and y value into y= mx+b with the slope value to find b.

5 0
3 years ago
Guys please help me with this question
sashaice [31]

Answer:

Step-by-step explanation:

\frac{g}{f} (x)=\frac{g(x)}{f(x)} \\=\frac{3x^2+x}{4x} \\=\frac{x(3x+1)}{4x} \\=\frac{3x+1}{4}

8 0
3 years ago
Can you please help me if you want I would give you brain list thanks have a good day!:)
olya-2409 [2.1K]

Answer:

the answer should maybe be -5, -4,-3

Step-by-step explanation:

either its being buggy or it wants you to put the numbers in a different way

8 0
3 years ago
Read 2 more answers
Other questions:
  • 3. Suppose your credit card has a balance of $7800 and an annual interest rate of 16%. You decide
    8·1 answer
  • If 3 dozen cookies require 1 cup of sugar, write a direct variation equation in two variables that represent this situation. Mak
    12·1 answer
  • Please help, multiple choice question
    14·1 answer
  • Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
    7·1 answer
  • The rectangle below has a area x^2-x-72 square meters and a length of x+8 meters what expression represents the width of the rec
    9·2 answers
  • Solve this equation<br> 3x^2 − 16x = x^2 − 30
    12·2 answers
  • . Mona swims a race in 28.872 seconds. What is her race time rounded to the nearest tenth of a second? 28.8
    10·2 answers
  • - 3c ( 4x - 2y ) PLESE HELP ASAP I WILL GIVE 5 STARS AND BRAINLIEST
    7·2 answers
  • Abelardo had 3 bags of apples. He gave 2 to his best friend, he gave 3 to his brother, and he fed 1 to his horse. On the way hom
    6·1 answer
  • Wich graph best represents a function with range -4 &lt; y &lt; 3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!