Write the following interval as an inequality.

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

Kisachek [45]

Answer: The number is: " 12 ".

____________________________________
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 .
______________________________________________
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 .
__________________________________________________
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 ".
__________________________________________

8 0

4 years ago

A rectangle has an area of 6x^(2) + 7x - 3 square units. Which of the following could represent the perimeter of the rectangle i

VLD [36.1K]

Answer:

Erm

Step-by-step explanation:

8 0

3 years ago

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What is the equation of the circle with center (4, 4) that passes through the point (10, 14)?

Katarina [22]

Answer:

Step-by-step explanation:

You use the given information in the standard form of a circle equation to solve for r. We have (h, k) which is the center and a point (x, y). The standard equation for a circle is

$(x-h)^2+(y-k)^2=r^2$

Filling in:

$(10-4)^2+(14-4)^2=r^2$ and

$6^2+10^2=r^2$ and

$r^2=136$

Now that we used the coordinate we don't need it anymore. x and y go back into the equation as x and y, not numbers. We do, however, need the center. Writing the equation:

$(x-4)^2+(y-4)^2=136$ which is choice D.

6 0

3 years ago

What was life like in Hargigo before people planted the mangrove trees?

Mamont248 [21]

Answer:

Step-by-step explanation:

That is until they met Dr. Gordon Sato who had an idea of how to help them. He proposed that Hargigo plant mangrove trees near the sea because ... From this one mangrove tree grew many, and these trees gave the people of Hargigo hope. ... They really brought the story of the mangrove trees to life.

4 0

3 years ago

A line goes through the point (6,–2) and has a slope of –3. What is the value of a if the point (a,7) lies on the line? A =

Sati [7]

Answer:

Step-by-step explanation:

Y = mx + b

slope(m) = 3/4

(3,7)...x = 3 and y = 7

now we sub...we r looking for b, the y int

7 = 3/4(3) + b

7 = 9/4 + b

7 - 9/4 = b

28/4 - 9/4 = b

19/4 = b

equation is : y = 3/4x + 19/4...lets put this in standard form

y = 3/4x + 19/4

-3/4x + y = 19/4...multiply by -4

3x - 4y = -19 <== standard form

if (x,5) is on the line

3x - 4y = -19.....sub in 5 for y

3x - 4(5) = -19

3x - 20 = -19

3x = -19 + 20

3x = 1

x = 1/3 <====so point a = (1/3,5)

4 0

4 years ago

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