Question

5) 2 + 3x| < 7;6) 2 – 5x| < 8.​

Answer 1

Ответ:

Пошаговое объяснение:

$|2+3x|$

x∈($-3;1\frac{2}{3}$)

|2-5x|<8

(2-5x)<8

-5x<6

x>-1.2

(2-5x)>-8

-5x>-10

x<2

x∈(-1.2;2)

Answer 2

To solve the inequalities:

5. 2 + 3x| < 7

First, let's consider two cases:

Case 1: When the expression inside the absolute value is positive: 2 + 3x < 7

Subtract 2 from both sides: 3x < 7 - 2 3x < 5

Divide both sides by 3 (since 3 is positive): x < 5/3

Case 2: When the expression inside the absolute value is negative: -(2 + 3x) < 7

Multiply both sides by -1 (this reverses the inequality): 2 + 3x > -7

Subtract 2 from both sides: 3x > -7 - 2 3x > -9

Divide both sides by 3 (since 3 is positive): x > -9/3 x > -3

Combining the results from both cases, we have:

x < 5/3 or x > -3

6. 2 - 5x| < 8

Again, we consider two cases:

Case 1: When the expression inside the absolute value is positive: 2 - 5x < 8

Subtract 2 from both sides: -5x < 8 - 2 -5x < 6

Divide both sides by -5 (since -5 is negative, we reverse the inequality): x > 6/-5 x > -6/5

Case 2: When the expression inside the absolute value is negative: -(2 - 5x) < 8

Multiply both sides by -1: 2 - 5x > -8

Subtract 2 from both sides: -5x > -8 - 2 -5x > -10

Divide both sides by -5 (since -5 is negative): x < -10/-5 x < 2

Combining the results from both cases, we have:

x > -6/5 or x < 2