A chess player played 44 games total. If he won 16 of the games, what is the ratio of games he lost to games he won?

What is the solution of ?<img src="https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D%20x-7%3D%5Cfrac%7B3%7D%7B4%7D%20x%2B14" id="Tex

Nonamiya [84]

Combine the terms by multiplying into a single fraction.

$\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 }$

Find the common denominator.

$\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14 }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14 }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14 }$

Combine the multiplied terms into a single fraction

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14 }$

Find the common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4} }$

Combine fractions with the lowest common denominator.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4} }$

Multiply the numbers.

$\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4} }$

Eliminate the denominators of the fractions.

$\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4} }$

Cancel the multiplied terms that are in the denominator.

$\bf{2(5x-14)=3x+56}$

To distribute.

$\bf{10x-28=3x+56 }$

Add 28 to both sides.

$\bf{10x-28+28=3x+56+28 }$

Simplify

$\bf{10x=3x+84 }$

Subtract 3x from both sides.

$\bf{10x-3x=3x+84-3x }$

Simplify

$\bf{7x=84 }$

Divide both sides by the same factor.

$\bf{x=\dfrac{84}{7} }$

Simplify

$\bf{x=12 \ \ \ === > \ \ \ Answer}$

↓

<h3>Verification</h3>

Let x=12.

$\bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3}{4}\times12+14 }$
$\bf{30-7=\dfrac{3\times12}{4}+14 }$
$\bf{30-7=\dfrac{36}{4}+14 }$
$\bf{30-7=9+14 }$
$\bf{23=9+14 }$
$\bf{23=23}$

Checked ✅

3 0

1 year ago

How do you solve 8x-7= 3x 9?

gtnhenbr [62]

8x - 7 = 3x + 9
8x - 3x = 9 + 7
5x = 16
x = 16/5 = 3 1/5

3 0

2 years ago

12 things that has energy

Lapatulllka [165]

Answer: Kinetic Energy Potential Energy Chemical Energy Elastic Energy Gravitational Energy Magnetic Energy Nuclear Energy Light Energy Radiant Energy Sound Energy Thermal Energy Mechanical Energy Electrical Energy

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

A quadratic function has zeros -7 and 9. What are the linear factors of the function?

garik1379 [7]

Answer:

(x+7)(x-9) = 0

Step-by-step explanation:

x + 7 = 0

x = -7

x - 9 = 0

x = 9

4 0

2 years ago

Suppose you have 20 coins that total $3.00. Some coins are nickels and some are quarters. Which of the following pairs of equati

shusha [124]

Answer: D. n + q = 20

5n + 25q = 300

Step-by-step explanation:

Let n represent the number of nickels that you have.

Let q represent the number of quarters that you have.

Suppose you have 20 coins. It means that

n + q = 20

The total value of the coins is $3. The value of a quarter is $0.25 and the value if a nickel is $0.05. Therefore, the equation would be

0.05n + 0.25q = 3

Multiplying both sides of the equation by 100, it becomes

5n + 25q = 300

The correct option is

D. n + q = 20

5n + 25q = 300

6 0

2 years ago