Verified answer

[(x – 7)/5 – 5/2 = (x + 9)/10]10

2(x-7)-5(5)=x+9

2x-14-25=x+9

2x-39=x+9

x=48

Since 5/2 does not have a variable to solve for move it to the right side by adding to both sides.

x-7/5 =5/2 + x+9/10

Mulitply 5/2 by 5/5 to get the denominator 10

x-7/5 =5/2 * 5/5+ x+9/10, then multiply the expression to create the LCD

x-7/5 =5(5)/10 + x+9/10, now you have numerators that can be combined

= x-7/5 =5(5) + x+9 /10

= x-7/5 =5 *5 + x+9 /10

= x-7/5 =25 + x+9 /10, add 9 to 25 to get;

= x-7/5 =34 + x /10 , reorder to get;

= x-7/5 =x +34 /10, there is one rational expression on each side

= (x-7) * 10 = (x + 34) * 5, multiply (x-7) by 10 to get

= 10 (x-7) = (x +34) * 5 multiply 10 by each term inside the ( )

= 10 (x) + 10(-7)= (x +34) * 5 multiply 10 by the x inside the ( )

= 10 * x + 10(-7)= (x +34) * 5

= 10x + 10(-7) = (x+34)*5

= 10x - 10 * 7 = (x+34)*5

= 10x - 70 = 5(x+34) mulitply 5 by each term inside ( )

= 10x - 70 = 5 (x) + 5(34) multiply 5 by the x insid the ( )

= 10x -70 = 5*x+5(34) multiply 5 by x to get 5x

= 10x -70 = 5x + 5(34)

= 10x -70 = 5x + 170 since -70 does not contain a variable move it to the right side of the equation

= 10x = 70 + 5x +170

= 10x = 240 + 5x move the variable 5x to the left side

= 10x - 5x = 240, x is a factor of both 10x and 5x so,

= (10 - 5) x = 240

= (5) x = 240

= 5x = 240, divide each term in the equation by 5

x = 240/5

x = 48

I know it's lengthy but hopefully the detailed step by step information will help you with future problems similar to or like this one

(x – 7)/5 – 5/2 = (x + 9)/10

10[(x – 7)/5 – 5/2] = 10[(x + 9)/10]

2x-14 -25= x+9

x-39=9

x=48

Yes, multiplying both sides by 10 makes solving easier.

x=48