Question

1) |15x-10|=5 2) |8x-6|=14
3)|8x+12|=20
4) |2x+14|=6
5) 2|x|+3|x|-18=|x|-7|x|+15
6) 7|x|-2|x|=3|x|+12
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Answer 1

$1) |15x - 10| = 5 \\ 1)15x - 10 = 5 \\ 15x = 5 + 10 \\ 15x = 15 \\ x = 15 \div 15 \\ x = 1 \\ 2) - 15x + 10 = 5 \\ - 15x = 5 - 10 \\ - 15x = - 5 \\ x = \frac{ - 5}{ - 15} \\ x = \frac{1}{3}$

$|8x - 6| = 14 \\ 1)8x - 6 = 14 \\ 8x = 14 + 6 \\ 8x = 20 \\ x = \frac{20}{8} = 2.5 \\ 2) - 8x + 6 = 14 \\ - 8x = 14 - 6 \\ - 8x = 8 \\ x = 8 \div ( - 8) = - 1$

$|8x + 12| = 20 \\ 1)8x + 12 = 20 \\ 8x = 20 - 12 \\ 8x = 8 \\ x = 8 \div 8 \\ x = 1 \\ 2) - 8x - 12 = 20 \\ - 8x = 20 + 12 \\ - 8x = 32 \\ x = 32 \div ( - 8) \\ x = - 4$

$|2x + 14| = 6 \\ 1)2x + 14 = 6 \\ 2x = 6 - 14 \\ 2x = - 8 \\ x = - 8 \div 2 \\ x = - 4 \\ 2) - 2x - 14 = 6 \\ - 2x = 6 + 14 \\ - 2x = 20 \\ x = 20 \div ( - 2) \\ x = - 10$

$2 |x| + 3 |x| - 18 = |x| - 7 |x| + 15 \\ 5 |x| + 7 |x| - |x| = 15 + 18 \\ 11 |x| = 33 \\ |x | = 33 \div 11 \\ |x| =3 \\ x1 = 3 \\ x2 = - 3$

$7 |x| - 2 |x| = 3 | x | + 12 \\ 5 |x| - 3 |x| = 12 \\ 2 |x| = 12 \\ |x| = 12 \div 2 \\ |x| = 6 \\ x1 = 6 \\ x2 = - 6$