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3 years ago

-4x+1=2x-17 What is the solution for x ?

Mathematics

1 answer:

katovenus [111]3 years ago

6 0

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{x = 3}}}}}$

Step-by-step explanation:

$\sf{ - 4x + 1 = 2x - 17}$

Move 2x to left hand side and change it's sign

Similarly, move 1 to right hand side and change it's sign

$\dashrightarrow{ \sf{ - 4x - 2x = - 17 - 1}}$

Collect like terms

$\dashrightarrow{ \sf{ - 6x = - 17 - 1}}$

The negative integers are always added but posses the negative ( - ) sign

$\dashrightarrow{ \sf{ - 6x = - 18}}$

Divide both sides by -6

$\dashrightarrow{ \sf{ \frac{ - 6x}{ - 6} = \frac{ - 18}{ - 6}}}$

Calculate

$\dashrightarrow{ \sf{x = 3}}$

Hope I helped!

Best regards! :D

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A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

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Answer:

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Step-by-step explanation:

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