Toán Lớp 7: rút gọn các biểu thức sau : 3(5x-2)-|x-5|, b:|2x+3|+2x+7, c: 3x-1+|1-3x|, d:3(x-1)-2|x+3|

Question

Toán Lớp 7:  rút gọn các biểu thức sau : 3(5x-2)-|x-5|, b:|2x+3|+2x+7, c: 3x-1+|1-3x|, d:3(x-1)-2|x+3|

ankim · Answer

$a) A= 3(5x-2)-|x-5|$   $x  geq 5 &rArr; |x-5|=x-5$   $&rArr;A=15x-6-(x-5)=15x-6-x+5=14x-1$   $x  leq 5 &rArr; |x-5| = 5-x$   $&rArr;A=15x-6-(5-x)=16x-11$   $b) B=|2x+3|+2x+7$   $x  geq  dfrac{-3}{2} &rArr; |2x+3|=2x+3$   $&rArr;B=2x+3+2x+7=4x+10$   $x  leq  dfrac{-3}{2} &rArr; |2x+3|=-2x-3$   $&rArr;B=-2x-3+2x+7=4$   $c) C=3x-1+|1-3x|$   $x  geq  dfrac{1}{3} &rArr; |1-3x|=3x-1$   $&rArr;C=3x-1+3x-1=6x-2$   $x  leq  dfrac{1}{3} &rArr; |1-3x|=-3x+1$   $&rArr;C=3x-1+(-3x+1)=3x-1-3x+1=0$   $d) D=3(x-1)-2|x+3|$   $x  geq -3 &rArr; |x+3|=x+3$   $&rArr; D=3x-3-2(x+3)=3x-3-2x-6=x-9$   $x  leq -3 &rArr; |x+3|=-(x+3)=-x-3$   $&rArr; D=3x-3-2(-x-3)=3x-3+2x+6=5x+3$

hongocha12 · Answer

Giải đáp+Lời giải và giải thích chi tiết: A=3(5x-2)-|x-5| x>=5=>x-5>=0 =>|x-5|=x-5 =>A=15x-6(x-5) =>A=14x-1 x<=5=>x-5<=0 =>|x-5|=5-x =>A=15x-6(5-x) =>A=15x-30+6x =>A=21x-30 b)B=|2x+3|+2x+7 x>=-3/2=>2x>=-3 =>2x+3>=0 =>|2x+3|=2x+3 =>B=2x+3+2x+7 =>B=4x+10 x<=-3/2=>2x<=-3 =>2x+3<=0 =>|2x+3|=-2x-3 =>B=-2x-3+2x+7=4 c)C=3x-1+|1-3x| x>=1/3=>3x>=1 =>3x-1>=0 =>|1-3x|=3x-1 =>C=3x-1+3x-1=6x-2 x<=1/3=>3x<=1 =>3x-1<=0 =>|1-3x|=-(3x-1) =>C=0 d)D=3(x-1)-2|x+3| x>=-3=>x+3>=0 =>2|x+3|=2(x+3)=2x+6 =>D=3x-3-2x-6=x-9 x<=-3=>x+3<=0 =>2|x+3|=-2(x+3)=-(2x+6) =>D=3x-3+2x+6=5x+3