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frosja888 [35]
2 years ago
12

Solve the equation X-5/6=-1/6

Mathematics
2 answers:
Gnom [1K]2 years ago
8 0

Answer:

  x = 2/3 = 0.667

Step-by-step explanation:

                 x = 2/3 = 0.667

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x+1/6-(5/6)=0  

Step by step solution :

Step  1  :

           5

Simplify   —

           6

Equation at the end of step  1  :

       1     5

 (x +  —) -  —  = 0  

       6     6

Step  2  :

           1

Simplify   —

           6

Equation at the end of step  2  :

       1     5

 (x +  —) -  —  = 0  

       6     6

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  6  as the denominator :

         x     x • 6

    x =  —  =  —————

         1       6  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 6 + 1     6x + 1

—————————  =  ——————

    6           6    

Equation at the end of step  3  :

 (6x + 1)    5

 ———————— -  —  = 0  

    6        6

Step  4  :

Adding fractions which have a common denominator :

4.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(6x+1) - (5)     6x - 4

————————————  =  ——————

     6             6    

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  6x - 4  =   2 • (3x - 2)  

Equation at the end of step  5  :

 2 • (3x - 2)

 ————————————  = 0  

      6      

Step  6  :

When a fraction equals zero :

6.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 2•(3x-2)

 ———————— • 6 = 0 • 6

    6    

Now, on the left hand side, the  6  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2  •  (3x-2)  = 0

Equations which are never true :

6.2      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

6.3      Solve  :    3x-2 = 0  

Add  2  to both sides of the equation :  

                     3x = 2

Divide both sides of the equation by 3:

                    x = 2/3 = 0.667

dusya [7]2 years ago
8 0

Answer:

X= 2/3

Step-by-step explanation:

x - 5/6 = -1/6

+5/6       +5/6

x = 2/3

You might be interested in
F(x)=(-3x+2) and g(x)=(2x^2-5x-1)
pashok25 [27]

Answer: -6x² + 15x + 5

Step-by-step explanation:

To solve this problem, you only need to substitute g(x)'s equation as the value of the x in f(x), then simplify.

Step 1: f(x) = -3(2x² - 5x - 1) + 2

Step 2: Apply the distributive property

-3(2x²) + -3(-5x) + -3(-1)

-6x² + 15x + 3

Step 3: Simplify

f(x) = -6x² + 15x + 3 + 2

f(x) = -6x² + 15x + 5

6 0
2 years ago
What is the unit rate for hours per task
timama [110]
What is the task and how many hours does it take?
4 0
2 years ago
X y
Darina [25.2K]

Answer:

Part 1) The rate of change is \frac{17}{15}

Part 2) The initial value is 68

Part 3) The function rule to the linear model is y=\frac{17}{15}x+68

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

step 1

Find the slope

take two points from the table

(0,68) and (15,85)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{85-68}{15-0}

m=\frac{17}{15}

In a linear function , the slope is the same that the rate of change

therefore

The rate of change is \frac{17}{15}

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the table

For x=0, y=68

therefore

The y-intercept is

b=68

The y-intercept is also called the initial value

therefore

The initial value is 68

step 3

Determine the function rule to the linear model

y=mx+b

we have

m=\frac{17}{15}

b=68

substitute

y=\frac{17}{15}x+68

8 0
3 years ago
Find the vertex, the axis of symmetry, and the y-intercept of the graph.
UNO [17]

<u>Given</u>:

Given that the graph of the parabola.

We need to determine the vertex, the axis of symmetry and the y - intercept of the graph.

<u>Vertex:</u>

The vertex of the parabola is the point at which the parabola changes its direction.

From the graph, it is obvious that the parabola changes its direction at the point (-2,0)

Hence, the vertex of the graph is (-2,0)

<u>Axis of symmetry:</u>

The axis of symmetry is the line that divides the parabola exactly into two equal halves.

Hence, from the graph, it is obvious the line x = -2 divides the graph exactly into two equal halves.

Hence, the axis of symmetry is x = -2.

<u>y - intercept:</u>

The y - intercept of the parabola is the value of y when x = 0.

In other words, the y - intercept of the graph is the value of y when the line passes through the y - axis.

Thus, from the graph it is obvious that when x = 0, the value of y is -3.

Hence, the y - intercept of the graph is -3.

6 0
3 years ago
Helppppp pleaseeee!!!!!!
maks197457 [2]
I got 3.825

your equation would be
(2x-1)(x+7)=72

when you distribute youd get
2x^2 +13x -7 =72

move the 72 over giving you
2x^2 +13x -79=0

i used the quadratic formula and the answer would be 3.825 because a negative answer wouldn’t make sense in this situation
5 0
2 years ago
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