Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-2(5x-\frac{2}{5})=7x+\frac{6}{5}\)
  2. \(-4(-3x+\frac{4}{7})=-5x+\frac{9}{10}\)
  3. \(-6(4x+\frac{5}{7})=-5x+\frac{2}{9}\)
  4. \(-4(4x-\frac{2}{3})=-7x+\frac{10}{3}\)
  5. \(4(5x+\frac{5}{3})=7x+\frac{3}{10}\)
  6. \(5(-4x-\frac{4}{9})=9x+\frac{10}{7}\)
  7. \(7(-4x+\frac{3}{8})=-9x+\frac{6}{5}\)
  8. \(-3(5x-\frac{5}{8})=-8x+\frac{3}{7}\)
  9. \(3(-2x-\frac{4}{7})=7x+\frac{10}{11}\)
  10. \(-7(-2x-\frac{3}{8})=3x+\frac{9}{2}\)
  11. \(-3(-2x-\frac{2}{7})=7x+\frac{4}{7}\)
  12. \(3(-2x-\frac{5}{7})=7x+\frac{7}{5}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-50}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -50x \color{red}{+4} & = & \color{red}{35x} +6 \\\Leftrightarrow & -50x \color{red}{+4} \color{blue}{-4} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-4} \\\Leftrightarrow & -50x-35x& = & 6-4 \\\Leftrightarrow & \color{red}{-85} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-85} & & \\\Leftrightarrow & x = \frac{-2}{85} & & \\ & V = \left\{ \frac{-2}{85} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{160}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-160} & = & \color{red}{-350x} +63 \\\Leftrightarrow & 840x \color{red}{-160} \color{blue}{+160} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{+160} \\\Leftrightarrow & 840x+350x& = & 63+160 \\\Leftrightarrow & \color{red}{1190} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1190} & & \\ & V = \left\{ \frac{223}{1190} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 14+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 284 \\\Leftrightarrow & x = \frac{284}{-1197} & & \\\Leftrightarrow & x = \frac{-284}{1197} & & \\ & V = \left\{ \frac{-284}{1197} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+8} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -48x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & -48x+21x& = & 10-8 \\\Leftrightarrow & \color{red}{-27} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-27} & & \\\Leftrightarrow & x = \frac{-2}{27} & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+200} & = & \color{red}{210x} +9 \\\Leftrightarrow & 600x \color{red}{+200} \color{blue}{-200} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{-200} \\\Leftrightarrow & 600x-210x& = & 9-200 \\\Leftrightarrow & \color{red}{390} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{390} & & \\ & V = \left\{ \frac{-191}{390} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{9})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-140} & = & \color{red}{567x} +90 \\\Leftrightarrow & -1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-567x} & = & \color{red}{567x} +90 \color{blue}{-567x} \color{blue}{+140} \\\Leftrightarrow & -1260x-567x& = & 90+140 \\\Leftrightarrow & \color{red}{-1827} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1827} & & \\\Leftrightarrow & x = \frac{-230}{1827} & & \\ & V = \left\{ \frac{-230}{1827} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{8})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+105} & = & \color{red}{-360x} +48 \\\Leftrightarrow & -1120x \color{red}{+105} \color{blue}{-105} \color{blue}{+360x} & = & \color{red}{-360x} +48 \color{blue}{+360x} \color{blue}{-105} \\\Leftrightarrow & -1120x+360x& = & 48-105 \\\Leftrightarrow & \color{red}{-760} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-760} & & \\\Leftrightarrow & x = \frac{3}{40} & & \\ & V = \left\{ \frac{3}{40} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{8})& = & -8x+\frac{3}{7} \\\Leftrightarrow & -15x+\frac{15}{8}& = & -8x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{+105} & = & \color{red}{-448x} +24 \\\Leftrightarrow & -840x \color{red}{+105} \color{blue}{-105} \color{blue}{+448x} & = & \color{red}{-448x} +24 \color{blue}{+448x} \color{blue}{-105} \\\Leftrightarrow & -840x+448x& = & 24-105 \\\Leftrightarrow & \color{red}{-392} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-392} & & \\\Leftrightarrow & x = \frac{81}{392} & & \\ & V = \left\{ \frac{81}{392} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{12}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-132} & = & \color{red}{539x} +70 \\\Leftrightarrow & -462x \color{red}{-132} \color{blue}{+132} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{+132} \\\Leftrightarrow & -462x-539x& = & 70+132 \\\Leftrightarrow & \color{red}{-1001} x& = & 202 \\\Leftrightarrow & x = \frac{202}{-1001} & & \\\Leftrightarrow & x = \frac{-202}{1001} & & \\ & V = \left\{ \frac{-202}{1001} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{24x} +36 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +36 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 112x-24x& = & 36-21 \\\Leftrightarrow & \color{red}{88} x& = & 15 \\\Leftrightarrow & x = \frac{15}{88} & & \\ & V = \left\{ \frac{15}{88} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+6} & = & \color{red}{49x} +4 \\\Leftrightarrow & 42x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 42x-49x& = & 4-6 \\\Leftrightarrow & \color{red}{-7} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-7} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x-\frac{15}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-75} & = & \color{red}{245x} +49 \\\Leftrightarrow & -210x \color{red}{-75} \color{blue}{+75} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+75} \\\Leftrightarrow & -210x-245x& = & 49+75 \\\Leftrightarrow & \color{red}{-455} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-455} & & \\\Leftrightarrow & x = \frac{-124}{455} & & \\ & V = \left\{ \frac{-124}{455} \right\} & \\\end{align}\)
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