Question

A) 4x-5 > 3x+7 г) (7x +1 22 2х + 3 6) |2x+7|≤|x-8 д) (4x-3|2|x + 6| в) 5|x-7| ​

Answer 1

It looks like you've provided a set of mathematical inequalities. I'll go through each one and solve them step by step:

A) 4x - 5 > 3x + 7

To solve this inequality, you want to isolate x on one side. Start by moving 3x to the left side by subtracting it from both sides:

4x - 3x - 5 > 7

Now, simplify:

x - 5 > 7

Add 5 to both sides:

x > 7 + 5 x > 12

So, the solution to this inequality is:

x > 12

B) (7x + 1) / (2x + 3) ≤ 6

To solve this inequality, first, multiply both sides by (2x + 3) to eliminate the denominator:

7x + 1 ≤ 6(2x + 3)

Now, distribute 6 on the right side:

7x + 1 ≤ 12x + 18

Next, move 7x to the left side by subtracting it from both sides:

1 ≤ 12x - 7x + 18

Simplify:

1 ≤ 5x + 18

Subtract 18 from both sides:

-17 ≤ 5x

Finally, divide by 5 (remember to reverse the inequality since you're dividing by a negative number):

-17/5 ≥ x

So, the solution to this inequality is:

x ≤ -17/5

C) (4x - 3)|2|x + 6||

It seems like this inequality is incomplete or there might be a formatting issue. Please provide the complete inequality for further assistance.

D) 5|x - 7|

This inequality represents an absolute value. Absolute value inequalities can have two cases, one for when the expression inside the absolute value is positive and one for when it's negative.

Case 1: (x - 7) is positive: x - 7 ≥ 0 x ≥ 7

Case 2: (x - 7) is negative: -(x - 7) ≥ 0 x - 7 ≤ 0 x ≤ 7

So, the solution to the absolute value inequality is:

x ≤ 7 or x ≥ 7

You can combine these two cases into one statement:

x ≠ 7

This means that x can be any real number except 7.