Question

7x-12>3x-205-2x>4x+ 29​

Answer 1

Ответ:

$1)7x - 12 > 3x - 20 \\ 7x - 3x - 12 > - 20 \\ 7x - 3x > - 20 + 12 \\ 4x > - 20 + 12 \\ 4x > - 8 \\ x > - 2$

$2)5 - 2x > 4x + 29 \\ 5 - 2x - 4x > 29 \\ - 2x - 4x > 29 - 5 \\ - 6 x > 29 - 5 \\ - 6x > 24 \\ x > - 4$

Ответ: -2;-4

Answer 2

To solve the given compound inequality, let's break it down into two separate inequalities:

1. 7x - 12 > 3x - 205

2. -2x > 4x + 29

Solving the first inequality: 7x - 12 > 3x - 205

First, let's simplify the equation by subtracting 3x from both sides: 7x - 3x - 12 > -205

Simplifying further: 4x - 12 > -205

Next, add 12 to both sides: 4x - 12 + 12 > -205 + 12

Simplifying: 4x > -193

Now, divide both sides by 4 (since the coefficient of x is 4 and we want to isolate x): (4x)/4 > -193/4

Simplifying: x > -193/4

So the solution to the first inequality is x > -193/4.

Moving on to the second inequality: -2x > 4x + 29

To solve this, let's first add 2x to both sides to get rid of the negative coefficient: -2x + 2x > 4x + 29 + 2x

Simplifying: 0 > 6x + 29

Now, subtract 29 from both sides: 0 - 29 > 6x + 29 - 29

Simplifying: -29 > 6x

Lastly, divide both sides by 6 (since the coefficient of x is 6 and we want to isolate x): (-29)/6 > (6x)/6

Simplifying: -29/6 > x

So the solution to the second inequality is x < -29/6.

Therefore, the overall solution to the compound inequality is: x > -193/4 and x < -29/6.