Question

2(3x-4)>4(x+1)-3 x(x - 4) - (x + 3)(x - 5) > - 5​

Answer 1

1)2(3х-4)>(х+1)-3

6х-8>(4х+4)-3

6х-8>4х-3+1

6х-4х>8-3+1

2х>6 |:2

х>3

2)то же уравнение

х^2-4х-(х^2-5х+3х-15)>-5

х^2-4х-х^2+5х-3х+15>-5 (х^2 сокращается)

-4х+5х-3х>-5

-2х>15-5

-2х>10 |:(-2)

х>-5

Answer 2

To solve the inequalities, let's work through them step by step:

1. $2(3x - 4) > 4(x + 1) - 3$

First, distribute on both sides:

$6x - 8 > 4x + 4 - 3$

Combine like terms:

$6x - 8 > 4x + 1$

Subtract $4x$ from both sides:

$2x - 8 > 1$

Add 8 to both sides:

$2x > 9$

Finally, divide by 2:

$x > 4.5$

So, the solution to the first inequality is $x > 4.5$.

2. $x(x - 4) - (x + 3)(x - 5) > -5$

First, expand the expressions:

$x^2 - 4x - (x^2 - 2x - 15) > -5$

Distribute the negative sign inside the second parentheses:

$x^2 - 4x - x^2 + 2x + 15 > -5$

Combine like terms:

$-2x + 15 > -5$

Subtract 15 from both sides:

$-2x > -20$

Divide by -2 (note that this reverses the inequality because we're dividing by a negative number):

$x < 10$

So, the solution to the second inequality is $x < 10$.

In summary, the solutions are:

1. $x > 4.5$
2. $x < 10$