First, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:
15x - 1 = color(red)(2)(5x - 2) + 815x−1=2(5x−2)+8
15x - 1 = (color(red)(2) xx 5x) - (color(red)(2) xx 2) + 815x−1=(2×5x)−(2×2)+8
15x - 1 = 10x - 4 + 815x−1=10x−4+8
15x - 1 = 10x + 415x−1=10x+4
Next, add color(red)(1)1 and subtract color(blue)(10x)10x from each side of the equation to isolate the xx term while keeping the equation balanced:
-color(blue)(10x) + 15x - 1 + color(red)(1) = -color(blue)(10x) + 10x + 4 + color(red)(1)−10x+15x−1+1=−10x+10x+4+1
(-color(blue)(10) + 15)x - 0 = 0 + 5(−10+15)x−0=0+5
5x = 55x=5
Now, divide each side of the equation by color(red)(5)5 to solve for xx while keeping the equation balanced:
(5x)/color(red)(5) = 5/color(red)(5)5x5=55
(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 1
x = 1
