Question

1)11+4х > 2х-7 2) 5-4х ≤ 7х+53)14+2 (-х+7) ≤ 24-3 (х-1)4)|х|+7 < 10

Answer 1

11+4х > 2х -7
2х > -18
х > -9
5 - 4х =< 7х - 5
0 =< 11х
х >= 0
14 +2(-х+7) =< 24 - 3(х-1)
14 + 14 - 2х =< 24+3 - 3х
28 - 2х =< 27 - 3х
1 <= -х
х >= 1
|х| + 7 <= 10
|х| <= 3
-3 < х < 3

Answer 2

Let's solve each inequality step by step:

1. 11 + 4x > 2x - 7

To solve this inequality, first, let's get all the x terms on one side and the constant terms on the other side:

11 + 4x - 2x > -7

Now, combine the x terms:

11 + 2x > -7

Next, isolate x by moving the constant term to the other side:

2x > -7 - 11 2x > -18

Finally, divide both sides by 2 to get the solution for x:

x > -9

So the solution for this inequality is x > -9.

2. 5 - 4x ≤ 7x + 5

First, let's get all the x terms on one side and the constant terms on the other side:

5 - 4x - 5 ≤ 7x

Now, combine the x terms:

-4x ≤ 7x

Next, isolate x by moving the 7x term to the other side. To do this, we can subtract 7x from both sides:

-4x - 7x ≤ 0

Combine the x terms:

-11x ≤ 0

Finally, divide both sides by -11. Since we are dividing by a negative number, the inequality sign will flip:

x ≥ 0

So the solution for this inequality is x ≥ 0.

3. 14 + 2(-x + 7) ≤ 24 - 3(x - 1)

First, distribute the multiplication:

14 - 2x + 14 ≤ 24 - 3x + 3

Combine the constant terms:

28 - 2x ≤ 27 - 3x

Next, move all the x terms to one side:

28 - 27 ≤ -3x + 2x

Simplify:

1 ≤ -x

Now, multiply both sides by -1 (don't forget to flip the inequality sign since we are multiplying by a negative number):

-1 ≥ x

So the solution for this inequality is x ≤ -1.

4. |x| + 7 < 10

To solve this inequality, split it into two cases:

Case 1: x is positive (x ≥ 0) |x| + 7 < 10 x + 7 < 10 x < 10 - 7 x < 3

Case 2: x is negative (x < 0) |x| + 7 < 10 -x + 7 < 10 7 < 10 + x 7 - 10 < x -3 < x

Since x is negative, the absolute value of x is the negation of x, so we have -x in the equation.

Combining the two cases, we get:

-3 < x < 3

So the solution for this inequality is -3 < x < 3.

Therefore, the solutions for the given inequalities are:

1. x > -9
2. x ≥ 0
3. x ≤ -1
4. -3 < x < 3