Question

РЕШИТЕ НЕРАВЕНСТВО относительно переменной х а(х-2)>х-1

Answer 1

a(x-2)>x-1

ax-2a-x+1>0

x(a-1)-2a+1>0

x(a-1)>2a-1

x>(2a-1)/(a-1)

Answer 2

Solving the Inequality

To solve the inequality a(x-2) > x-1 for the variable x, we can follow these steps:

1. Expand the inequality. 2. Simplify the inequality. 3. Solve for x.

Step 1: Expand the Inequality

The given inequality is a(x-2) > x-1. To solve for x, we first expand the inequality:

ax - 2a > x - 1 [[2 #]]

Step 2: Simplify the Inequality

Next, we simplify the inequality by rearranging the terms:

ax - x > 2a - 1 [[2 #]]

Step 3: Solve for x

Now, we can solve for x by isolating it on one side of the inequality:

x(a - 1) > 2a - 1 [[2 #]]

Finally, we can express x in terms of a:

x > (2a - 1) / (a - 1) [[2 #]]

So, the solution to the inequality a(x-2) > x-1 for the variable x is x > (2a - 1) / (a - 1).