Question

Решить неравенство 8-4x>x-2

Answer 1

8 - 4x > x - 2

-4x - x > -2 - 8

-5x > -10

x < 2

x ∈ (-∞; 2)

Answer 2

$8 - 4x > x - 2 \\ 8 - 4x - x + 2 > 0 \\ - 5x + 10 > 0 \\ - 5(x - 2) > 0 \\ x - 2 < 0 \\ x = ( - \infty ..2)$

х принадлежит промежутку (-бесконечности;2)

Answer 3

To solve the inequality $8-4x > x-2$, follow these steps:

Step 1: Move all $x$ terms to one side of the inequality and constant terms to the other side: $8 - 4x - x > -2.$

Step 2: Combine like terms: $8 - 5x > -2.$

Step 3: Move the constant term to the other side of the inequality: $8 > -2 + 5x.$

Step 4: Move the variable term to one side by subtracting $5x$ from both sides: $8 - 5x > -2.$

Step 5: Now, isolate the variable term by dividing both sides by $-5$ (and remember that when you divide or multiply an inequality by a negative number, the inequality sign flips): $x < \frac{-2}{-5}.$

Step 6: Simplify the right-hand side: $x < \frac{2}{5}.$

So, the solution to the inequality is $x < \frac{2}{5}$.