Question

18-8(x-2)<10-4x 19-7x<20-3(x-5) 2x-3(x+1)>2+x 3x-10(2+X)

Answer 1

Проверьте четвертое неравенство, оно не дописано
///Четвертое неравенство добавлено.

Answer 2

Let's solve each of these inequalities step by step:

1. $18 - 8(x - 2) < 10 - 4x$:

First, distribute the -8 on the left side:

$18 - 8x + 16 < 10 - 4x$

Now, combine like terms on both sides:

$34 - 8x < 10 - 4x$

Subtract 10 from both sides:

$24 - 8x < -4x$

Next, add 8x to both sides:

$24 < 4x$

Finally, divide both sides by 4 to isolate x:

$6 < x$

So, the solution is $x > 6$.

2. $19 - 7x < 20 - 3(x - 5)$:

First, distribute the -3 on the right side:

$19 - 7x < 20 + 3(5) - 3x$

Simplify the right side:

$19 - 7x < 20 + 15 - 3x$

Combine like terms:

$19 - 7x < 35 - 3x$

Now, add 7x to both sides:

$19 < 35 + 4x$

Subtract 35 from both sides:

$-16 < 4x$

Finally, divide both sides by 4 to isolate x:

$-4 < x$

So, the solution is $x > -4$.

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

First, distribute the -3 on the left side:

$2x - 3x - 3 > 2 + x$

Combine like terms on the left side:

$-x - 3 > 2 + x$

Add x to both sides:

$-3 > 2x + x$

Combine like terms:

$-3 > 3x$

Finally, divide both sides by 3 to isolate x:

$-1 > x$

So, the solution is $x < -1$.

4. $3x - 10(2 + x)$:

It appears that you didn't provide an inequality for the fourth expression. If you intended to include an inequality, please provide it, and I'll be happy to help you solve it.

Answer 3

Let's solve each of these inequalities step by step:

1. 18 - 8(x - 2) < 10 - 4x

First, distribute the -8 on the left side:

18 - 8x + 16 < 10 - 4x

Combine like terms on both sides:

-8x + 34 < 10 - 4x

Now, subtract 10 from both sides:

-8x + 34 - 10 < -4x

-8x + 24 < -4x

Now, subtract -4x from both sides:

-8x + 24 - 4x < 0

-12x + 24 < 0

Finally, subtract 24 from both sides:

-12x + 24 - 24 < 0 - 24

-12x < -24

Now, divide both sides by -12. When dividing by a negative number, remember to reverse the inequality:

-12x / -12 > -24 / -12

x > 2

So, the solution to the first inequality is x > 2.

2. 19 - 7x < 20 - 3(x - 5)

First, distribute the -3 on the right side:

19 - 7x < 20 - 3x + 15

Combine like terms on both sides:

-7x + 19 < 20 - 3x + 15

Now, subtract 20 and 15 from both sides:

-7x + 19 - 20 - 15 < -3x

-7x - 16 < -3x

Now, add 3x to both sides:

-7x - 16 + 3x < 0

-4x - 16 < 0

Finally, add 16 to both sides:

-4x - 16 + 16 < 0 + 16

-4x < 16

Now, divide both sides by -4. Remember to reverse the inequality when dividing by a negative number:

-4x / -4 > 16 / -4

x > -4

So, the solution to the second inequality is x > -4.

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

First, distribute the -3 on the left side:

2x - 3x - 3 > 2 + x

Combine like terms on both sides:

(2x - 3x) - 3 > (2 + x)

-x - 3 > 2 + x

Now, add x to both sides:

-x - 3 + x > 2 + x + x

-3 > 2x

Now, divide both sides by 2. Since dividing by a positive number, there's no need to reverse the inequality:

-3 / 2 > 2x / 2

-3/2 > x

So, the solution to the third inequality is x < -3/2.

4. 3x - 10(2 + x)

This is not an inequality but an expression. If you have any specific questions or need to set up an inequality involving this expression, please provide more information.