Question

8x + 12| = 20Б) |9x+ 15| = 6Г) 7|x| - 2|x| = 3x + 12​

Answer 1

Ответ:

1) 1   2) -1   3) 6

Пошаговое объяснение:

$1)8x + 12 = 20\\8x = 20 - 8\\8x = 8x\\x=\frac{8}{8} \\x=1\\\\2)9x+15=6\\9x = 6-15\\9x = -9x\\x=\frac{-9}{9} \\x = -1\\\\7x - 2x = 3x + 12\\7x - 2x - 3x = 12\\2x = 12\\x = \frac{12}{2}\\x = 6$

Answer 2

To solve these absolute value equations, you'll need to consider two cases for each equation: one where the expression inside the absolute value is positive and another where it's negative. Here are the solutions for each of your equations:

Б) |8x + 12| = 20:

Case 1: 8x + 12 is positive: 8x + 12 = 20 8x = 20 - 12 8x = 8 x = 8 / 8 x = 1

Case 2: 8x + 12 is negative: -(8x + 12) = 20 -8x - 12 = 20 -8x = 20 + 12 -8x = 32 x = 32 / -8 x = -4

So, the solutions for equation Б are x = 1 and x = -4.

Г) |9x + 15| = 6:

Case 1: 9x + 15 is positive: 9x + 15 = 6 9x = 6 - 15 9x = -9 x = -9 / 9 x = -1

Case 2: 9x + 15 is negative: -(9x + 15) = 6 -9x - 15 = 6 -9x = 6 + 15 -9x = 21 x = 21 / -9 x = -7/3

So, the solutions for equation Г are x = -1 and x = -7/3.

Д) 7|x| - 2|x| = 3x + 12:

Simplify the equation first:

5|x| = 3x + 12

Now, you'll again consider two cases:

Case 1: |x| is positive: 5x = 3x + 12 2x = 12 x = 12 / 2 x = 6

Case 2: |x| is negative: -5x = 3x + 12 -5x - 3x = 12 -8x = 12 x = 12 / -8 x = -3/2

So, the solutions for equation Д are x = 6 and x = -3/2.