Question

how to do equations with a variable on both sides x+3= -x - 5

Answer 1

Explanation: 
When we have variables on both sides we look for the coefficient that is lower than the two and reverse the sign. 

Example: 

1x+ 4 = 2x+3 

We reverse 1x sign because it is lower so we will be subtracting

2x-1x = 1x

1x+3=4 

We would then solve for x.

 

Let's begin to solve! 
Step 1:
You would look for the coefficient or variable that is less and reverse the sign. 

In this question the lower number is -x and so we would reverse the sign to add. 

x+x= 2

Step 2: 
We now have

2x+3 = -5

Step 3: 
We will subtract 3 to -5 to find X

-3+-5= -8

Step 4:
2x = -8

Divide both sides by two fo find x 

Our answer:

$\boxed{x = -4}$

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Summary:

We first looked for the lower coefficient (in this case variable). We then flipped the sign and solved for x. 

Answer 2

$x+3=-x-5$

When we have a variable on both sides, we want to find a way to move the variable so its only on one side, which will make it easier to solve the equation.

Add x to both sides of the equation to eliminate the "-x" on the right side of the equation.

$x+x+3=-x+x-5$

$2x+3=-5$

Subtract 3 from both sides

$2x+3-3=-5-3$

$2x=-8$

Divide 2 from both sides

$x=-4$

That is the solution. Have an awesome day! :)