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Анастасия4487
@Анастасия4487
August 2022
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ОЧЕНЬ СРОЧНО!!!!!!!!!!!!
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Мпрмггнпшоиол
4) a)|11 + 10x| = 1 ⇔ [ 11 + 10x = 1 ⇔ [ 10x = 1 - 11 = (-10) ⇔ [ x = (-10)/10 = (-1)
[ 11 + 10x = (-1) [ 10x = (-1) - 11 = (-12). [ x = (-12)/10 = (-6/5)
b)|7 - 3x| = 11 ⇔ [ 7 - 3x = 11 ⇔ [ -3x = 11 - 7 = 4 [ x = 4/(-3)
[ 7 - 3x = (-11) [ -3x = (-11) - 7 = (-18) ⇔ [ x = (-18)/(-3) = 6
5) a)|1+5x| ≤ 4 ⇔ { 1 + 5x ≤ 4 ⇔ { 5x ≤ 4 - 1 ≤ 3 { x ≤ 3/5
{ 1 + 5x ≥ (-4) { 5x ≥ (-4) - 1 ≥ (-5) ⇔ { x ≥ (-5)/5 ≥ (-1)
b)|2 - 9x| > 13 ⇔ { 2 - 9x > 13 { -9x > 13 - 2 > 11 { x > 11/(-9)
{ 2 - 9x < (-13) ⇔ { -9x < (-13) - 2 < (-15) ⇔ { x < (-15)/(-9) = 5/3
3) a){ 3 - 8x > 5 ⇔ { x < 1 { x < 1 { x < 1
{ x - 1 < 0 { -8x > 5 -3 > 2 ⇔ { x > 2/(-8) ⇔ { x < (-1/4)
b){ 6x +4 ≥ 0 { 6x ≥ (-4) { x ≥ (-4)/6 ≤ (-2/3)
{ 3x - 2 ≤ 1 ⇔ { 3x ≤ 1 + 2 ≤ 3 ⇔ { x ≤ 3/3 ≤ 1
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Answers & Comments
[ 11 + 10x = (-1) [ 10x = (-1) - 11 = (-12). [ x = (-12)/10 = (-6/5)
b)|7 - 3x| = 11 ⇔ [ 7 - 3x = 11 ⇔ [ -3x = 11 - 7 = 4 [ x = 4/(-3)
[ 7 - 3x = (-11) [ -3x = (-11) - 7 = (-18) ⇔ [ x = (-18)/(-3) = 6
5) a)|1+5x| ≤ 4 ⇔ { 1 + 5x ≤ 4 ⇔ { 5x ≤ 4 - 1 ≤ 3 { x ≤ 3/5
{ 1 + 5x ≥ (-4) { 5x ≥ (-4) - 1 ≥ (-5) ⇔ { x ≥ (-5)/5 ≥ (-1)
b)|2 - 9x| > 13 ⇔ { 2 - 9x > 13 { -9x > 13 - 2 > 11 { x > 11/(-9)
{ 2 - 9x < (-13) ⇔ { -9x < (-13) - 2 < (-15) ⇔ { x < (-15)/(-9) = 5/3
3) a){ 3 - 8x > 5 ⇔ { x < 1 { x < 1 { x < 1
{ x - 1 < 0 { -8x > 5 -3 > 2 ⇔ { x > 2/(-8) ⇔ { x < (-1/4)
b){ 6x +4 ≥ 0 { 6x ≥ (-4) { x ≥ (-4)/6 ≤ (-2/3)
{ 3x - 2 ≤ 1 ⇔ { 3x ≤ 1 + 2 ≤ 3 ⇔ { x ≤ 3/3 ≤ 1