Bài 4 trang 44 SGK Toán 8 Tập 2 Cánh diều - CD

a) Ta có:

\(\begin{array}{*{35}{l}} \frac{5x-2}{3}=\frac{5-3x}{2} \\ \Leftrightarrow \frac{2\left( 5x-2 \right)}{6}=\frac{3\left( 5-3x \right)}{6} \\ \Leftrightarrow 2\left( 5x-2 \right)=3\left( 5-3x \right) \\ \Leftrightarrow 10x-4=15-9x \\ \Leftrightarrow 10x+9x=15+4 \\ \Leftrightarrow 19x=19 \\ \Leftrightarrow x=19:19 \\ \Leftrightarrow x=1 \\ \end{array}\)

Vậy phương trình có nghiệm \(x = 1\).

b) Ta có:

\(\begin{array}{*{35}{l}} \frac{10x+3}{12}=1+\frac{6+8x}{9} \\ \Leftrightarrow \frac{3\left( 10x+3 \right)}{36}=\frac{36}{36}+\frac{4\left( 6+8x \right)}{36} \\ \Leftrightarrow 3\left( 10x+3 \right)=36+4\left( 6+8x \right) \\ \Leftrightarrow 30x+9=36+24+32x \\ \Leftrightarrow 30x+9=60+32x \\ \Leftrightarrow 30x-32x=60-9 \\ \Leftrightarrow -2x=51 \\ \Leftrightarrow x=-\frac{51}{2} \\ \end{array}\)

Vậy phương trình có nghiệm \(x = - \frac{{51}}{2}\).

c) Ta có:

\(\begin{array}{*{35}{l}} \frac{7x-1}{6}+2x=\frac{16-x}{5} \\ \Leftrightarrow \frac{5\left( 7x-1 \right)}{30}+\frac{30.2x}{30}=\frac{6\left( 16-x \right)}{30} \\ \Leftrightarrow 5\left( 7x-1 \right)+30.2x=6\left( 16-x \right) \\ \Leftrightarrow 35x-5+60x=96-6x \\ \Leftrightarrow 95x-5=96-6x \\ \Leftrightarrow 95x+6x=96+5 \\ \Leftrightarrow 101x=101 \\ \Leftrightarrow x=101:101 \\ \Leftrightarrow x=1 \\ \end{array}\)

-- Mod Toán 8 HỌC247