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3 years ago

What is the value of x in the equation 4x - 2(x + 3) = 8?

Mathematics

1 answer:

Bess [88]3 years ago

4 0

Answer:

x = 7

Step-by-step explanation:

The given equation is 4x - 2(x + 3) = 8. We need to find the value of x. The steps are as follows :

Firstly opening the bracket on the LHS,

4x -2x-6 = 8

Adding like terms together. So,

2x = 8+6

2x = 14

x = 7

So, the value of x is 7. Hence, the correct option is (d).

You might be interested in

Which of the following equations represents a linear function?

Sphinxa [80]

Answer:

Following equations represents a linear function:

y = 6x

y = 4x - √2

x – 4y = 6

Step-by-step explanation:

We know that a linear function is of the form

where m is the rate of change or slope and b is the y-intercept.

Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.

Now, let us check whether the given functions represent the linear functions or not.

Checking y = 6x

y = 6x

4 0

3 years ago

Solve using elimination<br> x+y-2z=8<br> 5x-3y+z=-6<br> -2x-y+4z=-13

Free_Kalibri [48]

So here is your answer with LaTeX issued format interpretation. Full process elucidated briefly, below:

$\begin{alignedat}{3}x + y - 2z = 8 \\ 5x - 3y + 2 = - 6 \\ - 2x - y + 4z = - 13 \end{alignedat}$

For this equation to get obtained under the impression of those variables we have to eliminate them individually for moving further and simplifying the linear equation with three variables along the axis.

Multiply the equation of x + y - 2z = 8 by a number with a value of 5; Here this becomes; 5x + 5y - 10z = 40; So:

$\begin{alignedat}{3}5x + 5y - 10z = 40 \\ 5x - 3y + z = - 6 \\ - 2x - y + 4z = - 13 \end{alignedat}$

Pair up the equations in a way to eliminate the provided variable on our side, that is; "x":

5x - 3y + z = - 6

-

5x + 5y - 10z = 40
______________

- 8y + 11z = - 46

Therefore, we are getting.

$\begin{alignedat}{3}5x + 5y - 10z = 40 \\ - 8y + 11z = - 46 \\ - 2x - y + 4z = - 13 \end{alignedat}$

Multiply the equation of 5x + 5y - 10z = - 40 by a number with a value of 2; Here this becomes; 10x + 10y - 20z = 80.

Multiply the equation of - 2x - y + 4z = - 13 by a number with a value of 5; Here this becomes; - 10x - 5y + 20z = - 65; So:

$\begin{alignedat}{3}10x + 10y - 20z = 80 \\ - 8y + 11z = - 46 \\ - 10x - 5y + 20z = - 65 \end{alignedat}$

Pair up the equations in a way to eliminate the provided variables on our side, that is; "x" and "z":

- 10x - 5y + 20z = - 65

+
10x + 10y - 20z = 80
__________________

5y = 15

$\begin{alignedat}{3}10x + 10y - 20z = 80 \\ - 8y + 11z = - 46 \\ 5y = 15 \end{alignedat}$

Multiply the equation of - 8y + 11z = - 46 by a number with a value of 5; Here this becomes; - 40y + 55z = - 230.

Multiply the equation of 5y = 15 by a number with a value of 8; Here this becomes; 40y = 120; So:

$\begin{alignedat}{3}10x + 10y - 20z = 80 \\ - 40y + 55z = - 690 \\ 40y = 120 \end{alignedat}$

Pair up the equations in a way to eliminate the provided variables on our side, that is; "y":

40y = 120

+

- 40y + 55z = - 230
_________________

55z = - 110

$\begin{alignedat}{3}10x + 10y - 20z = 80 \\ - 40y + 55z = - 230 \\ 55z = - 110 \end{alignedat}$

Solving for the variable of 'z':

$\mathsf{55z = - 110}$

$\bf{\dfrac{55z}{55} = \dfrac{-110}{55}}$

Cancel out the common factor acquired on the numerator and denominator, that is, "55":

$z = - \dfrac{\overbrace{\sout{110}}^{2}}{\underbrace{\sout{55}}_{1}}$

$\boxed{\mathbf{z = - 2}}$

Solving for variable "y":

$\mathbf{\therefore \quad - 40y - 55 \big(- 2 \big) = - 230}$

$\mathbf{- 40y - 55 \times 2 = - 230}$

$\mathbf{- 40y - 110 = - 230}$

$\mathbf{- 40y - 110 + 110 = - 230 + 110}$

Adding the numbered value as 110 into this equation (in previous step).

$\mathbf{- 40y = - 120}$

Divide by - 40.

$\mathbf{\dfrac{- 40y}{- 40} = \dfrac{- 120}{- 40}}$

$\mathbf{y = \dfrac{- 120}{- 40}}$

$\boxed{\mathbf{y = 3}}$

Solve for variable "x":

$\mathbf{10x + 10y - 20z = 80}$

$\mathbf{Since, \: z = - 2; \quad y = 3}$

$\mathbf{10x + 10 \times 3 - 20 \times (- 2) = 80}$

$\mathbf{10x + 10 \times 3 + 20 \times 2 = 80}$

$\mathbf{10x + 30 + 20 \times 2 = 80}$

$\mathbf{10x + 30 + 40 = 80}$

$\mathbf{10x + 70 = 80}$

$\mathbf{10x + 70 - 70 = 80 - 70}$

$\mathbf{10x = 10}$

Divide by this numbered value $\mathbf{10}$ to get the final value for the variable "x".

$\mathbf{\dfrac{10x}{10} = \dfrac{10}{10}}$

The numbered values in the numerator and the denominator are the same, on both the sides. This will mean the "x" variable will be left on the left hand side and numbered values "10" will give a product of "1" after the division is done. On the right hand side the numbered values get divided to obtain the final solution for final system of equation for variable "x" as "1".

$\boxed{\mathbf{x = 1}}$

Final solutions for the respective variables in the form of " (x, y, z) " is:

$\boxed{\mathbf{\underline{\Bigg(1, \: \: 3, \: \: - 2 \Bigg)}}}$

Hope it helps.

8 0

3 years ago

Read 2 more answers

Calculate the time required for an object to increase velocity from 25 ft/s to 125 ft/s. Use the formula V = V0 + 32t, where V0

Alborosie

Using the equation of motion:
$V=V_0+32t$

Plug in the final velocity: $V=125$
and the initial velocity: $V_0=25$

Then you would get:
$125=25+32t\\
125-25=32t\\
100=32t\\
t= \frac{25}{8} \\
t=3.125$

8 0

3 years ago

All whole numbers greater than 0 are also called the ____________ integers.

mars1129 [50]

Answer: positive integers

Step-by-step explanation:

All whole numbers greater than 0 are also called the positive integers.

6 0

3 years ago

Read 2 more answers

A streamer goes downstream from point A to B in 9hrs .from B to A ,upstream it takes 10h .if the speed is 1km/hr , what will be

MA_775_DIABLO [31]

Answer:

$Speed\ of\ streamer\ in\ still\ water=19\ km/hr\\\\Distance=180\ km$

Step-by-step explanation:

$Let\ speed\ of\ steamer\ in\ still\ water=x\ km/hr\\\\Let\ distance\ between\ A\ and\ B=d\ km$

Downstream:

$Speed of stream=1\ km/hr\\\\Downstream\ speed=speed\ of\ steamer+speed\ of\ stream\\\\Downstream\ speed=x+1\\\\Time\ Taken=9\ hrs\\\\Distance=d\\\\Distance=speed\times time\\\\d=(x+1)\times 9\\\\d=9x+9\ ..................................................eq(1)$

Upstream:

$Speed of stream=1\ km/hr\\\\Upstream\ speed=speed\ of\ steamer-speed\ of\ stream\\\\Downstream\ speed=x-1\\\\Time\ Taken=10\ hrs\\\\Distance=d\\\\Distance=speed\times time\\\\d=(x-1)\times 9\\\\d=10x-10\ ..................................................eq(2)$

$From\ eq(1)\ and\ eq(2)\\\\10x-10=9x+9\\\\10x-9x=10+9\\\\x=19\\\\from\ equation\ 2\\\\d=10x-10\\\\d=10\times 19-10=190-10\\\\d=180$

$Speed\ of\ streamer\ in\ still\ water=19\ km/hr\\\\Distance=180\ km$

3 0

3 years ago