Question

What is 2/3x+4=4/5x-2

Answer 1

Hey there!

Apply  fraction cross multiply: if a/b = c/d , then  a *d = b*c

2 ( 5x - 2 ) = ( 2x + 4 ) * 4

expand : 2 (5x-2 )  => 2*5x - 2*2 => 10x - 4

expand : ( 2x +4 ) * 4 =>  2x * 4 + 4*4 => 8x + 16

10x - 4 = 8x+16

add 4 to both sides:

10x-4+4 = 8x+16+4

simplify :

10x  = 8x + 20

subtract 8x from both sides:

10x -8x = 8x+20-8x

simplify:

2x = 20

Therefore:

x = 20 / 2

x = 10

Hope that helps!

Answer 2

Step 1. Simplify 2/3x to 2x/3

2x/3 + 4 = 4/5x - 2

Step 2. Simplify 4/5x to 4x/5

2x/3 + 4 = 4x/5 - 2

Step 3. Multiply both sides by 15 (the LCM of 3,5)

10x + 60 = 12x - 30

Step 4. Subtract 10x from both sides

60 = 12x - 30 - 10x

Step 5. Simplify 12x - 30 - 10x to 2x - 30

60 =2x - 30

Step 6. Add 30 to both sides

60 + 30 =2x

Step 7. Simplify 60 + 30 to 90

90 = 2x

Step 8. Divide both sides by 2

90/2 = x

Step 9.  Simplify 90/2 to 45

45 = x

Step 10. Switch sides

x = 45