Bài 2:
a: \(720:\left[41-\left(2x+5\right)\right]=2^3\cdot5\)
=>\(720:\left[41-\left(2x+5\right)\right]=8\cdot5=40\)
=>\(41-\left(2x+5\right)=\dfrac{720}{40}=18\)
=>2x+5=41-18=23
=>2x=23-5=18
=>x=18/2=9
b: \(\left(5x-25\right)\cdot3+144:2^2=66\)
=>\(\left(5x-25\right)\cdot3+\dfrac{144}{4}=66\)
=>\(15\left(x-5\right)+36=66\)
=>\(15\left(x-5\right)=30\)
=>x-5=2
=>x=7
c: \(148-45:\left(7x-4\right)=147\)
=>\(45:\left(7x-4\right)=148-147=1\)
=>7x-4=45
=>7x=49
=>x=49/7=7
d: \(\left(3x+2\right)\cdot7^3=2\cdot7^4\)
=>\(\left(3x+2\right)=\dfrac{2\cdot7^4}{7^3}=2\cdot7=14\)
=>3x=14-2=12
=>x=12/3=4
e: \(\left(5^2+3^2\right)\cdot x+\left(5^2-3^2\right)x=10^2\)
=>\(x\left(5^2+3^2+5^2-3^2\right)=100\)
=>\(x\cdot\left(25+25\right)=100\)
=>50x=100
=>x=2
f: \(\left(x-3\right)^3=27\)
=>\(\left(x-3\right)^3=3^3\)
=>x-3=3
=>x=6
g: \(4\cdot5^{x-2}=500\)
=>\(5^{x-2}=\dfrac{500}{4}=125\)
=>\(5^{x-2}=5^3\)
=>x-2=3
=>x=5
h: \(x-\left(-7\right)=-5-14\)
=>x+7=-19
=>x=-19-7
=>x=-26
i: \(18-x=-8-\left(-13\right)\)
=>\(18-x=-8+13=5\)
=>x=18-5=13
j: \(45-\left(x+17\right)=-26\)
=>\(x+17=45-\left(-26\right)=45+26=71\)
=>x=71-17=54
Bài 3:
a: -5<x<8
mà x nguyên
nên \(x\in\left\{-4;-3;-2;-1;0;1;2;3;4;5;6;7\right\}\)
Tổng các số nguyên x thỏa mãn -5<x<8 là:
\(\left(-4\right)+\left(-3\right)+\left(-2\right)+...+4+5+6+7\)
\(=\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0+5+6+7\)
=5+6+7
=12+6
=18
b: -15<=x<14
mà x nguyên
nên \(x\in\left\{-15;-14;-13;...;12;13\right\}\)
Tổng các số nguyên x thỏa mãn là:
\(\left(-15\right)+\left(-14\right)+\left(-13\right)+...+11+12+13\)
\(=\left(-15\right)+\left(-14\right)+\left(-13+13\right)+\left(-12+12\right)+...+\left(-1+1\right)+0\)
=-15-14
=-29
\(a,720:\left[41-\left(2x+5\right)\right]=2^3\cdot5\\ \Rightarrow720:\left[41-\left(2x+5\right)\right]=40\\ \Rightarrow41-\left(2x+5\right)=720:40\\ \Rightarrow41-\left(2x+5\right)=18\\ \Rightarrow2x-5=41-18\\ \Rightarrow2x-5=23\\ \Rightarrow2x=23+5\\ \Rightarrow2x=28\\ \Rightarrow x=\dfrac{28}{2}=14\)
`b,(5x-25)* 3+144:2^2=66`
`=>(5x-25)* 3+144:4=66`
`=>(5x-25)* 3+36=66`
`=> (5x-25)* 3=66-36`
`=> (5x-25)* 3=30`
`=> 5x-25=30:3`
`=>5x-25=10`
`=> 5x=10+25`
`=>5x=35`
`=>x=35/5=7`
`c,148-45:(7x-4)=147`
`=> 45:(7x-4)=148-147`
`=> 45:(7x-4)=1`
`=> 7x-4=45:1`
`=> 7x-4=45`
`=> 7x=45+4`
`=>7x=49`
`=>x=49/7=7`
`d, (3x+2) * 7^3 = 2*7^4`
`=> 3x+2=2* 7^4:7^3`
`=>3x+2=2*7`
`=>3x+2=14`
`=> 3x=14-2`
`=>3x=12`
`=>x=12/3=4`
`e, (5^2 +3^2) x+(5^2-3^2)x=10^2`
`=> ( 25+9) x + (25-9)x=100`
`=> 34x+16x=100`
`=> ( 34+16)x=100`
`=> 50x=100`
`=>x=100:50`
`=>x= 2`
`f, (x-3)^3=27`
`=>(x-3)^3=3^3`
`=>x-3=3`
`=>x=3+3`
`=>x=6`
