Bài 1:
a: 2x-4=0
=>2x=4
=>\(x=\dfrac{4}{2}=2\)
b: 6-2x=0
=>2x=6
=>\(x=\dfrac{6}{2}=3\)
c: 0,25x-1=0
=>0,25x=1
=>\(x=1:0,25=4\)
d: \(4,9-0,7x=0\)
=>0,7x=4,9
=>\(x=\dfrac{4.9}{0.7}=7\)
e: \(\dfrac{2}{5}x+1=\dfrac{4}{5}\)
=>\(\dfrac{2}{5}x=\dfrac{4}{5}-1=-\dfrac{1}{5}\)
=>\(x=-\dfrac{1}{5}:\dfrac{2}{5}=-\dfrac{1}{5}\cdot\dfrac{5}{2}=-\dfrac{1}{2}\)
f: \(-\dfrac{1}{2}x+2=\dfrac{5}{2}x-1\)
=>\(-\dfrac{1}{2}x-\dfrac{5}{2}x=-1-2\)
=>\(-3x=-3\)
=>3x=3
=>\(x=\dfrac{3}{3}=1\)
h: \(-\dfrac{1}{2}\left(2x+1\right)+\dfrac{1}{2}=x-1\)
=>\(-x-\dfrac{1}{2}+\dfrac{1}{2}=x-1\)
=>-x=x-1
=>-2x=-1
=>x=1/2
g: 3x+2=2x-3
=>3x-2x=-3-2
=>x=-5
Bài 2:
Thay x=4 vào phương trình, ta được:
\(m^2+5\cdot4=6\cdot4-3\)
=>\(m^2=24-3-20=1\)
=>\(\left[{}\begin{matrix}m=1\\m=-1\end{matrix}\right.\)
Bài 3:
Vận tốc chạy là 2x(km/h)
Độ dài quãng đường đi bộ là \(x\cdot1=x\left(km\right)\)
30p=0,5(giờ)
Độ dài quãng đường bạn Hà chạy là \(0,5\cdot2x=x\left(km\right)\)
Phương trình ta có sẽ là:
x+x=5
Bài 4:
a: \(\dfrac{2\left(x-3\right)}{4}-\dfrac{1}{2}=\dfrac{6x+9}{3}-2\)
=>\(\dfrac{x-3}{2}-\dfrac{1}{2}=2x+3-2\)
=>\(\dfrac{x-4}{2}=2x+1\)
=>2(2x+1)=x-4
=>4x+2=x-4
=>3x=-6
=>x=-2
b: \(\dfrac{2\left(3x+1\right)+1}{4}-5=\dfrac{2\left(3x-1\right)}{5}-\dfrac{3x+2}{10}\)
=>\(\dfrac{6x+3}{4}-5=\dfrac{6x-2}{5}-\dfrac{3x+2}{10}\)
=>\(\dfrac{5\left(6x+3\right)}{20}-\dfrac{100}{20}=\dfrac{4\left(6x-2\right)-2\cdot\left(3x+2\right)}{20}\)
=>5(6x+3)-100=4(6x-2)-2(3x+2)
=>30x+15-100=24x-8-6x-4
=>30x-85=18x-12
=>12x=-12+85=73
=>\(x=\dfrac{73}{12}\)
c: \(\dfrac{x}{3}+\dfrac{x-2}{4}=0,5x-2,5\)
=>\(\dfrac{4x+3\left(x-2\right)}{12}=0,5x-2,5\)
=>7x-6=12(0,5x-2,5)
=>7x-6=6x-30
=>7x-6x=-30+6
=>x=-24
d: \(\dfrac{x-4}{3}-\dfrac{x-3}{4}=\dfrac{x-2}{5}-\dfrac{x-1}{6}\)
=>\(\dfrac{20\left(x-4\right)-15\left(x-3\right)}{60}=\dfrac{12\left(x-2\right)-10\left(x-1\right)}{60}\)
=>20x-80-15x+45=12x-24-10x+10
=>5x-35=2x-14
=>3x=-14+35=21
=>x=21:3=7
