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2 years ago

Are the equations 6x-6=3x and x-1=3x equivalent?

Mathematics

1 answer:

expeople1 [14]2 years ago

4 0

Answer:

No, they aren't the same (equivalent).

Step-by-step explanation:

First, solve for both equations:

Equation #1: 6x-6=3x

Simplifying

6x + -6 = 3x

Reorder the terms:

-6 + 6x = 3x

Solving

-6 + 6x = 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-6 + 6x + -3x = 3x + -3x

Combine like terms: 6x + -3x = 3x

-6 + 3x = 3x + -3x

Combine like terms: 3x + -3x = 0

-6 + 3x = 0

Add '6' to each side of the equation.

-6 + 6 + 3x = 0 + 6

Combine like terms: -6 + 6 = 0

0 + 3x = 0 + 6

3x = 0 + 6

Combine like terms: 0 + 6 = 6

3x = 6

Divide each side by '3'.

x = 2

Simplifying

Equation #2: x-1=3x

Simplifying

x + -1 = 3x

Reorder the terms:

-1 + x = 3x

Solving

-1 + x = 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-1 + x + -3x = 3x + -3x

Combine like terms: x + -3x = -2x

-1 + -2x = 3x + -3x

Combine like terms: 3x + -3x = 0

-1 + -2x = 0

Add '1' to each side of the equation.

-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0

0 + -2x = 0 + 1

-2x = 0 + 1

Combine like terms: 0 + 1 = 1

-2x = 1

Divide each side by '-2'.

x = -0.5

Simplifying

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Read 2 more answers

For the linear function f(x) = -2x+1 , find the following

Leya [2.2K]

Given:

The function is:

$f(x)=-2x+1$

To find:

a. Slope and Y-intercept.

b. Is the function increasing, decreasing, or constant, justify your answer.

c. Graph the function, label x, and y-intercepts.

Solution:

a. We have,

$f(x)=-2x+1$ ...(i)

The slope intercept form of a line is:

$y=mx+b$ ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

$m=-2,b=1$

Therefore, the slope of the line is -2 and the y-intercept is 1.

b. If the slope of a linear function is negative, then the function is decreasing.

If the slope of a linear function is positive, then the function is increasing.

If the slope of a linear function is 0, then the function is constant.

The slope of the linear function is negative.

Therefore, the function is decreasing.

c. We have,

$f(x)=-2x+1$

At $x=0$ , we get

$f(0)=-2(0)+1$

$f(0)=1$

So, the y-intercept is at (0,1).

At $f(x)=0$ , we get

$0=-2x+1$

$2x=1$

$x=\dfrac{1}{2}$

$x=0.5$

So, the x-intercept is at $\left(0.5,0\right)$ .

Plot the points $(0,1), \left(0.5,0\right)$ and connect them by a straight line as shown below:

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3 years ago

Are the equations 6x-6=3x and x-1=3x equivalent?​

Are the equations 6x-6=3x and x-1=3x equivalent?