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solve: 6x+13=4x+21

solve the equation

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Patricia G. | Family ESL or Spanish Teacher; Corporate ESL/English CoachFamily ESL or Spanish Teacher; Corporate...
4.5 4.5 (21 lesson ratings) (21)
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Original question:  6x + 13 = 4x + 21 

Step 1: Subtract 21 from both sides:    6x -21 + 13 = 4x +21 - 21 

      Result 1: 6x - 8 = 4x

Step 2:  Subtract 6x from both sides:   6x - 6x - 8 = 4x - 6x

      Result 2:  -8= -2x

Step 3: Divide both sides by -2:    -8/-2 = -2x/-2

      Result 3: Remember that a negative number divided by a negative number = a positive, so... 

                                                  4=x

 

 

Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)
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Hi, Hailey.

To solve equations, you want to get the variable by itself on one side of the equation. You have to undo what is being done to the variable, and you have to do the same thing to both sides of the equation.

In this equation, we have terms with x on both sides, so we need to move one of them:

 6x + 13 = 4x + 21
-4x           -4x              do the same thing to both sides
2x + 13 =  21              4x - 4x is zero, we don't need to write it because 0 + 21 is 21

We now need to move the 13 away from the x-term:

2x + 13 = 21
      -13   -13
2x  = 8

x is multiplied by 2, so we divide each side by 2:

2x = 8
2      2

x = 4

You can plug 4 into the original equation to check it:

6(4) + 13 = 4(4) + 21

24 + 13 = 16 + 21

37 = 37

It works. Hope this helps!

Kayla W. | Elementry to University Mathematics TutorElementry to University Mathematics Tuto...
4.9 4.9 (69 lesson ratings) (69)
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6x+13 =4x+21

6x+13-13=4x+21-13

6x=4x+8

6x-4x=8

2x=8

(2/2)x=8/2

x=2

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