Giải các phương trình sau:
a, $\frac{3x+2}{2}$ – $\frac{3x+1}{6}$ = $\frac{5}{3}$ + 2x
b, $\frac{x+4}{5}$ – x +4 = $\frac{x}{3}$ – $\frac{x-2}{2}$
c, $\frac{4x+3}{5}$ – $\frac{6x-2}{7}$ = $\frac{5x+4}{3}$ + 3
d, $\frac{5x+2}{6}$ – $\frac{8x-1}{3}$ = $\frac{4x+2}{5}$ -5
`a)( 3x+2)/2 – (3x+1)/6 = 5/3 + 2x`
`⇔3(3x+2)−3x−1=10+12x`
`⇔9x+6−3x−1=10+12x`
`⇔6x+5=10+12x`
`⇔6x=-5`
`⇔x=-5/6`
`b)(x+4)/5 – x +4 = x/3 – (x-2)/2`
`⇔6(x+4)−30x+120=10x−15(x−2)`
`⇔6x+24−30x+120=10x−15x+30`
`⇔19x=114`
`⇔x=6`
`c)(4x+3)/5 – ( 6x-2)/7 = (5x+4)/3 + 3`
`⇔21(4x+3)−30(3x−1)=35(5x+4)+315`
`⇔84x+63−90x+30=175x+140+315`
`⇔181x=−362`
`⇔x=-2`
`d)(5x+2)/6 – ( 8x-1)/3 = (4x+2)/5 -5`
`⇔5(5x+2)−10(8x−1)=12(2x+1)−150`
`⇔25x+10−80x+10=24x+12−150`
`⇔79x=158`
`⇔x=2`
Đáp án:
d) x=2
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{3\left( {3x + 2} \right) – 3x – 1}}{6} = \dfrac{{2.5 + 2x.6}}{6}\\
\to 9x + 6 – 3x – 1 = 10 + 12x\\
\to 6x = – 5\\
\to x = – \dfrac{5}{6}\\
b)\dfrac{{6\left( {x + 4} \right) – 30x + 4.30}}{{30}} = \dfrac{{10x – 15\left( {x – 2} \right)}}{{30}}\\
\to 6x + 24 – 30x + 120 = 10x – 15x + 30\\
\to 19x = 114\\
\to x = 6\\
c)\dfrac{{21\left( {4x + 3} \right) – 15\left( {6x – 2} \right)}}{{5.3.7}} = \dfrac{{35\left( {5x + 4} \right) + 3.105}}{{5.3.7}}\\
\to 84x + 63 – 90x + 30 = 175x + 140 + 315\\
\to 181x = – 362\\
\to x = – 2\\
d)\dfrac{{5\left( {5x + 2} \right) – 10\left( {8x – 1} \right) – 6\left( {4x + 2} \right) + 5.30}}{{30}} = 0\\
\to 25x + 10 – 80x + 10 – 24x – 12 + 150 = 0\\
\to 79x = 158\\
\to x = 2
\end{array}\)