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

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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

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

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

2x-33=4x+6x

-33=2x+6x

-33=8x

-33/8=x

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

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

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.

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

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

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!

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

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