Question

7x-3(x-6) > 5x+912x - 2(3 - 2x)< 2(x-2)​

Answer 1

Ответ:

$7x - 3(x - 6) > 5x + 9 \\ 7x - 3x + 6 > 5x + 9 \\ 7x - 3x - 5x > 9 - 6 \\ - x > 3 \\ x < - 3$

$12x - 2(3 - 2x) < 2(x - 2) \\ 12x - 6 + 4x < 2x - 4 \\ 12x + 4x - 2x < - 4 + 6 \\ 14x < 2 \\ x < 2 \div 14 \\ x < \frac{1}{7}$

Answer 2

To solve the inequalities, let's simplify and solve them step by step:

1. $7x - 3(x - 6) > 5x + 9$

   Distribute the -3 inside the parentheses:

   $7x - 3x + 18 > 5x + 9$

   Combine like terms:

   $4x + 18 > 5x + 9$

   Subtract $4x$ from both sides:

   $18 > x + 9$

   Subtract $9$ from both sides:

   $9 > x$

   So, $x < 9$.

2. $2x - 2(3 - 2x) < 2(x - 2)$

   Distribute the -2 inside the parentheses on the left side:

   $2x - 6 + 4x < 2x - 4$

   Combine like terms:

   $6x - 6 < 2x - 4$

   Subtract $2x$ from both sides:

   $4x - 6 < -4$

   Add $6$ to both sides:

   $4x < 2$

   Divide both sides by $4$ (note that $4$ is positive, so the inequality direction doesn't change):

   $x < \frac{1}{2}$

   So, $x < \frac{1}{2}$.

In summary:

1. For the first inequality, $x$ must be less than 9: $x < 9$.
2. For the second inequality, $x$ must be less than $1/2$: $x < \frac{1}{2}$.