What is the solution to this equation?1. 2x+45-78=4x+6x-0

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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2x+45-78=4x+6x-0

For this first one, the first thing you have to do is get the variables on one side and the numbers on the other.  So let's subtract 2x from each side.

45-78 = 4x + 6x - 2x

-33 = 8x

x = -33/8

 

67-77x=0

This one is easier because we don't even have to do any kind of addition or subtraction.  We just subtract 67 from both sides.

-77x = -67

Then divide both sides by -77

x = 67/77

 

87+99-2y+y=56y

 

This one is done just the same as the first one.  Try it yourself.  The answer you should come up with is

y = 186/57

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

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2x+45-78=4x+6x-0

2x-33=4x+6x-0

2x-33=4x+6x

-33=2x+6x

-33=8x

-33/8=x

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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2x + 45 - 78 = 4x + 6x - 0

First combine the like terms, ( 45 with -78, and 4x with 6x )

By combining the like terms, your equation should look like

2x - 33 = 10x now, subtract 2x on both sides

By subtracting, your equation should look like

-33 = 8x Now, divide both sides by 8

By dividing, your equation should look like

-33/8 = x which is your answer

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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2x + 45 - 78 = 4x + 6x - 0 

Simplify both sides : 

2x - 33 = 10x 

Bring variable terms to one side and numbers to the other side : 

10x - 2x = -33

8x = -33

The way to undo multiplication is division so : 

x = -33/8

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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2x+45-78=4x+6x-0

so you simplify what you can on both sides

2x+33=10x

subtract 2x from both sides

33=8X

X= 33/8, or 4 and 1/8. 

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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2x+45-78=4x+6x-0

combine like terms

2x-33=10x

bring like terms on the same side

-33=10x-2x

-33=8x

divice by 8

`-33/8 = (8x)/8  `

x=`-33/8 ` or -4.125

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

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2x+45-78=4x+6x-0

2x-33=10x-0

2x-33+33=10x-0+33

2x=10x+33

2x-10x=10x+33-10x

-8x=33

-8x/-8=33/-8

x=-33/8

jenner1256's profile pic

jenner1256 | High School Teacher | (Level 1) eNoter

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1. 2x + 45 - 78 = 4x + 6x - 0

The -0 doesn't change the value and is not necessary.(I'll keep it in case you need it, though.)

First, combine like terms on each side of the equation.

2x + 45 - 78 = 4x + 6x - 0

2x - 33 = 10x - 0

Second, move the variables (letters) to one side - with their coefficients,  of course.*You can do this in 2 steps or one.

(Remember that anything you do to one side of the equation must be done to the other side & that the sides are split by the equal sign.)

2x - 33 = 10x - 0

-2x           -2x

-33 = 8x - 0

+0          +0

-33 = 8x     OR 8x = -33


Third, Isolate the variable -- divide to solve.

8x = -33

8x/8 = -33/8

x = -33/3

 

2. 67-77x=0

Don't need first step in this problem.

Second

67 -77x = 0 OR 67 -77x = 0

-67           -67                       +77x   +77x

-77x = -67               OR 67 = 77x

Third

-77x = -67               OR 67 = 77x

-77x/-77 = -67/-77  OR 67/77 = 77x/77

x = -67/-77= 67/77 OR 67/77 = x

 

3. 87 + 99 - 2y + y = 56y

First

87 + 99 - 2y + y = 56y  (y is just 1y)

186       - y          =56y  (-y can be written as -1y)

Second

186 - y = 56y

+y      +y

186 = 57y

Third

186/57 = 57y/57

186/57 = y

** Remember on tests especially: you can always but that answer back in for "X" in the original problem & both sides will be equal!

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

 

To solve

1. 2x+45-78=4x+6x-0

Solution:

This is a linear equation in one variable x. We solve such equations by simple operations like adding equals to,des , or subtracting equals  , or multiplying by  equals or dividing both by equals both sides of the equality and in order to bring x's to one side and numbers to the other side and express the x in terms of a number.

2x+45-78 = 4x+6x-0, Simplify clollecthe like terms together on each side:

2x-33 =10x.

2x-10x-33 = 10x-10x, subtracted 10 x from both sides.

-8x-33+33= 0+33. Added 33 to both sides.

-8x =33.

x = 33/(-8) = -33/8. Divide both sides by -8

 

2. 67-77x=0

67-77x= 0.

67-67-77x=0-66. Subtracted 66 from both sides.

-77x= -66. Simplified both sides.

x=-66/(-77). Divided both sides by -77.

x=6/7.  Simplified to the  smallest equivalent form of fraction.

3. 87+99-2y+y=56y

186-y = 56y.Simplified by collecting like terms on both sides.

186-y+y = 56y+y. To bring y's to one side and numbers to the other side we added y to both sides.So,

186 = 57y.

186/57  = 57y/57. Divide by 57 both sides.

Or 197/57 = y.Or

y =186/57

arzuka's profile pic

arzuka | College Teacher | (Level 1) eNoter

Posted on

 

here are the answers to your algebraic problems...

1. 2x+45-78=4x+6x-0

2x-33=10x+0

2x-10x=33+0

-8x=33

8x=-33

x=-33/8= -4.125

2. 67-77x=0

-77x=-67

77x=67

x=67/77=0.87

3. 87+99-2y+y=56y

186-2y+y=56y

-y-56y=-186

-57y=-186

57y=186

y=186/57

y=3.26

 

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