การประยุกต์ของสมการเชิงเส้นตัวแปรเดียว ม.2 แบบฝึกหัด 3.1 ทบทวนการแก้สมการ การแก้สมการแบบย้ายข้าง

การประยุกต์ของสมการเชิงเส้นตัวแปรเดียว ม.2 แบบฝึกหัด 3.1 ทบทวนการแก้สมการ

การแก้สมการแบบย้ายข้าง วีดีโอการแก้สมการ แบบย้ายข้าง

	จงแก้สมการต่อไปนี้ พร้อมทั้งแสดงวิธีตรวจสอบคำตอบ
...	$\color{blue}\large\begin{array}{rcl}1.\; \; \;\; \; 3x - \frac{2}{5} &= & 7+2x\\\\3x - 2x -\frac{2}{5} &= & 7\\\\x -\frac{2}{5} &= & 7\\\\x &= & 7+\frac{2}{5}\\\\x&= & \frac{35+2}{5}\\\\x &= & \frac{37}{5}\\\\x&= & 7\frac{2}{5}\\\\\end{array}$
	$\color{blue}\large\begin{array}{rcl}2.\; \; \;\; \;\frac{1}{2}+6y &= & -4y\\\\6y &= & -4y-\frac{1}{2}\\\\6y+4y &= & -\frac{1}{2}\\\\10y &= & -\frac{1}{2}\\\\y &= & -\frac{1}{2}\times \frac{1}{10}\\\\y &= & -\frac{1}{20}\\\\\end{array}$
	$\color{blue}\large\begin{array}{rcl}3.\; \; \; \; \; 10x-1-7x+3 &= & 7x-10\\\\3x+2 &= & 7x-10\\\\3x -7x+2 &= & -10\\\\-4x+2 &= & -10\\\\-4x &= & -10-2\\\\-4x &= & -12\\\\x &= & \frac{-12}{-4}\\\\x &= & 3\end{array}$
	$\color{blue}\large\begin{array}{rcl}4.\; \; \; \; \; 2.7x + 2.2 &= & 2.4x-2.6\\\\2.7x -2.4x + 2.2 &= & -2.6\\\\0.3x + 2.2 &= & -2.6\\\\0.3x &= & -2.6 - 2.2\\\\0.3x &= & -4.8\\\\x &= & -\frac{4.8}{0.3}\\\\x &= & -1.6\end{array}$ วีดีโอการแก้สมการ แบบย้ายข้าง Adobe Flash Player not installed or older than 9.0.115!
	$\color{blue}\large\begin{array}{rcl}5.\; \; \; \; \; 1.5x + 2+2.5x-0.5 &= & 4x-1.5-3x\\\\2.7x -2.4x + 2.2 &= & -2.6\\\\0.3x + 2.2 &= & -2.6\\\\0.3x &= & -2.6 - 2.2\\\\0.3x &= & -4.8\\\\x &= & -\frac{4.8}{0.3}\\\\x &= & -1.6\end{array}$
	$\color{blue}\large\begin{array}{rcl}6.\: \: \: \: \: 2(x-3) &= & x+15\\\\2x-6 &= & x+15\\\\2x-x-6 &= & 15\\\\x-6 &= & 15\\\\x &= & 15+6\\\\x &= & 21\end{array}$
	$\color{blue}\large\begin{array}{rcl}7.\; \; \; \; \; 3(y+2) &= & y-1\\\\3y+6 &= & y-1\\\\3y-y+6 &= & -1\\\\2y &= & -1-6\\\\2y &= & -7\\\\y &= & -\frac{7}{2}\\\\\end{array}$
	$\color{blue}\large\begin{array}{rcl}8.\; \; \; \; \; 0 &= & 3(3-2x)+5(x-1)\\\\0 &= & 9-6x+5x-5\\\\0 &= & 4-x\\\\x &= & 4\end{array}$
	$\color{blue}\large\begin{array}{rcl}9.\;\; \; \; \; 5(2-3y)-15 &= &-y-7\\\\10-15y-15 &= &-y-7\\\\-15y-5 &= &-y-7\\\\-15y &= &-y-7+5\\\\-15y &= &-y-2\\\\-15y+y &= &-2\\\\-14y&= &-2\\\\y&= &\frac{-2}{-14}\\\\y&= &\frac{1}{7}\\\\\end{array}$
	$\color{blue}\large\begin{array}{rcl}10.\; \; \; \; \; -11y+4(y-3)+6y &= & 4y-12\\\\-11y+4y-12+6y &= & 4y-12\\\\-y-12 &= & 4y-12\\\\-4y-y-12 &= & -12\\\\-5y-12 &= & -12\\\\-5y &= & -12+12\\\\-5y &= & 0\\\\y &= & 0\end{array}$
	$\color{blue}\large\begin{array}{rcl}11.\; \; \; \; \; \frac{3}{4}x + \frac{5}{2}x&= & 0\\\\(\frac{3}{4} + \frac{5}{2})x&= & 0\\\\(\frac{3+10}{4} )x&= & 0\\\\(\frac{13}{4} )x&= & 0\\\\x&= & 0\times \frac{4}{13}\\\\x&= & 0\end{array}$ วีดีโอการแก้สมการ แบบย้ายข้าง Adobe Flash Player not installed or older than 9.0.115!
	$\color{blue}\large\begin{array}{rcl}12.\; \; \; \; \; \frac{a}{2}+ \frac{a}{3}&= & -5\\\\(\frac{3+2}{6} )a&= & -5\\\\(\frac{5}{6} )a&= & -5\\\\a &= & -5\times \frac{6}{5}\\\\a &= & -6\\\\\end{array}$
	$\color{blue}\large\begin{array}{rcl}13.\; \; \; \; \; \frac{3}{4}x - \frac{5}{2}x&= & -7\\\\(\frac{3}{4} + \frac{5}{2})x&= & -7\\\\(\frac{3+10}{4} )x&= & -7\\\\(\frac{13}{4} )x&= & -7\\\\x&= & -7\times \frac{4}{13}\\\\x&= & -\frac{28}{13}\\\\x&= & -2\frac{2}{13}\end{array}$
	$\color{blue}\large\begin{array}{rcl}14.\; \; \; \; \; \frac{a}{3}+ \frac{13}{6}&= & 3- \frac{a}{2}\\\\\frac{a}{3}+ \frac{a}{2}+ \frac{13}{6}&= & 3\\\\(\frac{3+2}{6} )a+\frac{13}{6}&= & 3\\\\(\frac{5}{6} )a &= &3- \frac{13}{6}\\\\(\frac{5}{6} )a &= & \frac{18-18}{6}\\\\(\frac{5}{6} )a &= & 0\\\\a &= & 0\times \frac{6}{5} \\\\a &= & 0\end{array}$
	$\color{blue}\large\begin{array}{rcl}15.\; \; \; \; \; \frac{1}{2}y+ \frac{3}{4}y&= & 7+\frac{2}{3}y\\\\\frac{1}{2}y+ \frac{3}{4}y -\frac{2}{3}y&= & 7\\\\\frac{6y+9y-8y}{12}&= & 7\\\\\frac{7}{12}y&= & 7\\\\y&= & 7\times \frac{12}{7}\\\\y&= & 12\end{array}$
	$\color{blue}\large\begin{array}{rcl}16.\; \; \;\; \; \frac{x}{2}-\frac{x}{4}&= & x-9\\\\\frac{x}{2}-\frac{x}{4}-x&= & -9\\\\(\frac{1}{2}-\frac{1}{4}-1)x&= & -9\\\\(\frac{2-1-4}{4})x&= & -9\\\\(-\frac{3}{4})x&= & -9\\\\x&= & -9\times -\frac{4}{3}\\\\x&= &12\end{array}$ วีดีโอการแก้สมการ แบบย้ายข้าง Adobe Flash Player not installed or older than 9.0.115!
	$\color{blue}\large\begin{array}{rcl}17.\; \; \;\; \; \frac{a-1}{3}+3&= & \frac{a+14}{9}\\\\\frac{a-1}{3}-\frac{a+14}{9}&= & -3\\\\\frac{3(a-1)-(a+14)}{9}&= & -3\\\\\frac{3a-3-a-14}{9}&= & -3\\\\\frac{2a-17}{9}&= & -3\\\\\frac{2a}{9}-\frac{17}{9}&= & -3\\\\\frac{2}{9}a&= &\frac{17}{9}-3\\\\\frac{2}{9}a&= &\frac{17-27}{9}\\\\a&= &-\frac{10}{9}\times \frac{9}{2}\\\\a&= &-5\end{array}$
	$\color{blue}\large\begin{array}{rcl}18.\; \; \;\; \;2(7+3x)-6(x+2)&= & x\\\\14+6x-6x-12-x&= & 0\\\\-x+2&= &0\\\\-x&= &-2\\\\x&= &2\end{array}$ วีดีโอการแก้สมการ แบบย้ายข้าง Adobe Flash Player not installed or older than 9.0.115!
	$\color{blue}\large\begin{array}{rcl}19.\; \; \;\; \; 2.4a-4.2(a+1)&= & 1.1a+10.3\\\\2.4a-4.2a-4.2&= & 1.1a+10.3\\\\1.8a-4.2&= & 1.1a+10.3\\\\1.8a -1.1a&= & 10.3+4.2\\\\-2.9a&= & 14.5\\\\a&= & -\frac{14.5}{2.9}\\\\a&= &-5\end{array}$
	$\color{blue}\large\begin{array}{rcl}20.\; \; \;\; \; 4.5(2-3x)+0.8x&= & 2.3(x+30)\\\\9-13.5x+0.8x&= & 2.3x+69\\\\-12.7x-2.3x&= & 69-9\\\\-15x&= & 60\\\\x&= & -\frac{60}{15}\\\\x&= &-4\end{array}$
	$\color{blue}\large\begin{array}{rcl}21.\; \; \;\; \; 0.12y-1.6(y-2)&= & 6.8-1.28y\\\\0.12y-1.6y-3.2+1.28y&= & 6.8\\\\0.2y-3.2&= & 6.8\\\\0.2y&= & 6.8+3.2\\\\y&= & \frac{10}{0.2}\\\\y&= &50\end{array}$
	$\color{blue}\large\begin{array}{rcl}22.\; \; \;\; \; \frac{2x-5}{2}+\frac{4-x}{4}&= & \frac{1}{4}+x\\\\\frac{2(2x-5)+4-x}{4}&= & \frac{1}{4}+x\\\\\frac{4x-10+4-x}{4}&= & \frac{1}{4}+x\\\\\frac{3x-6}{4}&= & \frac{1}{4}+x\\\\\frac{3x}{4}-\frac{6}{4}-x&= & \frac{1}{4}\\\\\frac{3x}{4}-x&= & \frac{1}{4}+\frac{6}{4}\\\\(\frac{3}{4}-1)x&= & \frac{7}{4}\\\\(\frac{3-4}{4})x&= & \frac{7}{4}\\\\(-\frac{1}{4})x&= & \frac{7}{4}\\\\x&= & \frac{7}{4}\times (-4)\\\\x&= &-7\end{array}$
	$\color{blue}\large\begin{array}{rcl}23.\; \; \;\; \; \frac{a+7}{3}-(2-a)&= & \frac{a-5}{6}\\\\\frac{a+7}{3}-\frac{a-5}{6}+a&= &2\\\\\frac{a}{3}+\frac{7}{3}-\frac{a}{6}+\frac{5}{6}+a&= &2\\\\\frac{a}{3}-\frac{a}{6}+a&= &2-\frac{7}{3}-\frac{5}{6}\\\\\frac{2a-a+6a}{6}&= & \frac{12-14-5}{6}\\\\\frac{7}{6}a&= & -\frac{7}{6}\\\\a&= & -\frac{7}{6}\times \frac{6}{7}\\\\a&= &-1\end{array}$ วีดีโอการแก้สมการ แบบย้ายข้าง Adobe Flash Player not installed or older than 9.0.115!
	$\color{blue}\large\begin{array}{rcl}24.\; \; \; \; \; \frac{2x}{15}+ \frac{x+6}{12}&= & \frac{3}{10}(x+15)\\\\\frac{2x}{15}+\frac{x}{12}+\frac{6}{12}&= & \frac{3}{10}x+\frac{45}{10}\\\\\frac{2x}{15}+\frac{x}{12}-\frac{3}{10}x &= & \frac{9}{2}-\frac{1}{2}\\\\\frac{8x+5x-18x}{60}&= & \frac{9}{2}-\frac{1}{2}\\\\-\frac{5}{60}x&= &\frac{8}{2}\\\\-\frac{1}{12}x&= & 4\\\\x&= & 4\times (-12)\\\\x&= & -48\end{array}$
	$\color{blue}\large\begin{array}{rcl}25.\; \; \; \; \; \frac{5m}{6}- \frac{3m-1}{4}&= & 2m-\frac{6-m}{3}\\\\\frac{5m}{6}- \frac{3m}{4}+\frac{1}{4}&= & 2m-\frac{6}{3}+\frac{m}{3}\\\\\frac{5m}{6}- \frac{3m}{4}-2m -\frac{m}{3}&= & -\frac{6}{3}-\frac{1}{4}\\\\\frac{10m-9m-24m-4m}{12}&= & \frac{-3-24}{12}\\\\-\frac{27}{12}m&= & -\frac{27}{12}\\\\-\frac{9}{4}m&= & -\frac{9}{4}\\\\m&= & -\frac{9}{4}\times -\frac{4}{9}\\\\m&= & 1\end{array}$
	$\color{blue}\normalsize\begin{array}{rcl}26.\; \; \;\; \;\frac{2x-5}{2}-\frac{5+3x}{4}&= & \frac{2x-1}{2}-\frac{5x-2}{8}\\\\\frac{2x}{2}-\frac{5}{2}-\frac{5}{4}-\frac{3x}{4}&= & \frac{2x}{2}-\frac{1}{2}-\frac{5x}{8}+\frac{2}{8}\\\\x-\frac{5}{2}-\frac{5}{4}-\frac{3x}{4}&= & x-\frac{1}{2}-\frac{5x}{8}+\frac{1}{4}\\\\x-x-\frac{3x}{4}+\frac{5x}{8}&= &\frac{5}{2}-\frac{1}{2}+\frac{1}{4}+\frac{5}{4}\\\\-\frac{3x}{4}+\frac{5x}{8}&= &\frac{10-2+1+5}{4}\\\\\frac{-6x+5x}{8}&= & 14\\\\-\frac{x}{8}&= & 14\\\\x&= & 14\times (-8)\\\\x&= &-112\end{array}$
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