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Two thirds of a number decreased by six is two. what is the number?

Kisachek [45]

Answer: The number is: " 12 ".

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Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
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Method 1)

Add "6" to EACH SIDE of the equation;
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→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
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Multiply each side of the equation by " $\frac{3}{2}$ " ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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→ $\frac{3}{2}$ * $\frac{2}{3}$ x = 8 * $\frac{3}{2}$ ;

→ x = 8 * $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 .
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x = 12 .
______________________________________________
Method 2)
______________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:
→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
 → 3 * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3}{1}$ * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3*2}{1*3}$ x = 8 * 3
→ $\frac{6}{3}$ x = 24 ;

→ 2x = 24 ;

→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :

2x / 2 = 24 / 2 ;

x = 12 .
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Method 3).
__________________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Now, divide each side of the equation by " $\frac{2}{3}$ " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ $\frac{2}{3}$ x } / { $\frac{2}{3}$ } = 8 / { $\frac{2}{3}$ } ;

to get: x = 8 / { $\frac{2}{3}$ } ;

= 8 * ( $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 ;
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x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
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At the point where:
___________________________________________
= 8 * ( $\frac{3}{2}$ ) ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;
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We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
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{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
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and we can rewrite the expression:
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$\frac{8}{1}$ * $\frac{3}{2}$ ;
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as: $\frac{4}{1}$ * $\frac{3}{1}$ ;
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which equals:
__________________________________________
→ $\frac{4*3}{1*1}$ ;

= $\frac{12}{1}$ ;

= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
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8 0

4 years ago

If ln=54 and lm =31 then mn =?

lina2011 [118]

1,643 bc of multiplying or 85 bc of adding but I'm pretty sure it's multiplying

8 0

3 years ago

Read 2 more answers

(4,2) rotated 180° counterclockwise around the orgin

jonny [76]

Answer: -4, -2

Step-by-step explanation: The formula for a 180 degree counterclockwise rotation is x,y -> -x, -y. You change the sign for both numbers, so they both become negative.

Hope this helped!

5 0

4 years ago

Read 2 more answers

At the arcade, Sami won 2 blue tickets, 1 yellow ticket, and 3 red tickets for 1500 total points. Jamie won 1 blue ticket, 2 yel

aleksandrvk [35]

Answer:

$\left[\begin{array}{ccc}2&1&3\\1&2&2\\2&3&1\end{array}\right]$ $\left[\begin{array}{c}b&y&r\end{array}\right]$ $= \left[\begin{array}{c}1500&1225&1200\end{array}\right]$

Step-by-step explanation:

Given

$b = blue$

$y = yellow$

$r = red$

Required

Represent as a matrix

For Sammy:

$2\ blue + 1\ yellow + 3\ red =1500$

So, we have:

$2b + 1y + 3r = 1500$

$2b + y + 3r = 1500$

For Jamie:

$1\ blue + 2\ yellow + 2\ red =1225$

So, we have:

$1b + 2y + 2r = 1225$

$b + 2y + 2r = 1225$

For Yvonne:

$2\ blue + 3\ yellow + 1\ red =1200$

So, we have:

$2b + 3y + 1r = 1200$

$2b + 3y + r = 1200$

The system of equations are:

$2b + y + 3r = 1500$

$b + 2y + 2r = 1225$

$2b + 3y + r = 1200$

To represent as a matrix, we have:

$\left[\begin{array}{ccc}b_1&y_1&r_1\\b_2&y_2&r_2\\b_3&y_3&r_3\end{array}\right]$ $\left[\begin{array}{c}b&y&r\end{array}\right]$ $= \left[\begin{array}{c}Total_1&Total_2&Total_3\end{array}\right]$

This gives:

$\left[\begin{array}{ccc}2&1&3\\1&2&2\\2&3&1\end{array}\right]$ $\left[\begin{array}{c}b&y&r\end{array}\right]$ $= \left[\begin{array}{c}1500&1225&1200\end{array}\right]$

3 0

3 years ago

Decimals, fractions, and percents can all represent the same values. True OR False

Margaret [11]

True. Decimals can be put into fraction form which can be put into fraction form, then put into percentage form. Vice versa

6 0

3 years ago

Read 2 more answers