Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{21x} +8 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & 36x-21x& = & 8-8 \\\Leftrightarrow & \color{red}{15} x& = & 0 \\\Leftrightarrow & x = \frac{0}{15} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{+192} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 960x \color{red}{+192} \color{blue}{-192} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{-192} \\\Leftrightarrow & 960x+280x& = & 35-192 \\\Leftrightarrow & \color{red}{1240} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{1240} & & \\ & V = \left\{ \frac{-157}{1240} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{-220x} +20 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{+220x} & = & \color{red}{-220x} +20 \color{blue}{+220x} \color{blue}{+132} \\\Leftrightarrow & 495x+220x& = & 20+132 \\\Leftrightarrow & \color{red}{715} x& = & 152 \\\Leftrightarrow & x = \frac{152}{715} & & \\ & V = \left\{ \frac{152}{715} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & 6x+\frac{7}{5} \\\Leftrightarrow & 25x-\frac{25}{11}& = & 6x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{-125} & = & \color{red}{330x} +77 \\\Leftrightarrow & 1375x \color{red}{-125} \color{blue}{+125} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{+125} \\\Leftrightarrow & 1375x-330x& = & 77+125 \\\Leftrightarrow & \color{red}{1045} x& = & 202 \\\Leftrightarrow & x = \frac{202}{1045} & & \\ & V = \left\{ \frac{202}{1045} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+12} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 264x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & 264x+55x& = & 5-12 \\\Leftrightarrow & \color{red}{319} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{319} & & \\ & V = \left\{ \frac{-7}{319} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{18}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-36} \\\Leftrightarrow & -120x-50x& = & 45-36 \\\Leftrightarrow & \color{red}{-170} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-170} & & \\\Leftrightarrow & x = \frac{-9}{170} & & \\ & V = \left\{ \frac{-9}{170} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{11})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{20}{11}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x- \frac{180}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{-180} & = & \color{red}{693x} +22 \\\Leftrightarrow & 1485x \color{red}{-180} \color{blue}{+180} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{+180} \\\Leftrightarrow & 1485x-693x& = & 22+180 \\\Leftrightarrow & \color{red}{792} x& = & 202 \\\Leftrightarrow & x = \frac{202}{792} & & \\\Leftrightarrow & x = \frac{101}{396} & & \\ & V = \left\{ \frac{101}{396} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -8x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{-100} & = & \color{red}{-560x} +49 \\\Leftrightarrow & -1050x \color{red}{-100} \color{blue}{+100} \color{blue}{+560x} & = & \color{red}{-560x} +49 \color{blue}{+560x} \color{blue}{+100} \\\Leftrightarrow & -1050x+560x& = & 49+100 \\\Leftrightarrow & \color{red}{-490} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-490} & & \\\Leftrightarrow & x = \frac{-149}{490} & & \\ & V = \left\{ \frac{-149}{490} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{7})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 24x+\frac{18}{7}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{105x} +49 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{-105x} & = & \color{red}{105x} +49 \color{blue}{-105x} \color{blue}{-54} \\\Leftrightarrow & 504x-105x& = & 49-54 \\\Leftrightarrow & \color{red}{399} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{399} & & \\ & V = \left\{ \frac{-5}{399} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-90} & = & \color{red}{231x} +22 \\\Leftrightarrow & -990x \color{red}{-90} \color{blue}{+90} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+90} \\\Leftrightarrow & -990x-231x& = & 22+90 \\\Leftrightarrow & \color{red}{-1221} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-1221} & & \\\Leftrightarrow & x = \frac{-112}{1221} & & \\ & V = \left\{ \frac{-112}{1221} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-120} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -1320x \color{red}{-120} \color{blue}{+120} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+120} \\\Leftrightarrow & -1320x+275x& = & 66+120 \\\Leftrightarrow & \color{red}{-1045} x& = & 186 \\\Leftrightarrow & x = \frac{186}{-1045} & & \\\Leftrightarrow & x = \frac{-186}{1045} & & \\ & V = \left\{ \frac{-186}{1045} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{12})& = & 2x+\frac{3}{10} \\\Leftrightarrow & 35x+\frac{35}{12}& = & 2x+\frac{3}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{2100}{ \color{blue}{60} }x+ \frac{175}{ \color{blue}{60} })& = & (\frac{120}{ \color{blue}{60} }x+ \frac{18}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 2100x \color{red}{+175} & = & \color{red}{120x} +18 \\\Leftrightarrow & 2100x \color{red}{+175} \color{blue}{-175} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{-175} \\\Leftrightarrow & 2100x-120x& = & 18-175 \\\Leftrightarrow & \color{red}{1980} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{1980} & & \\ & V = \left\{ \frac{-157}{1980} \right\} & \\\end{align}\)
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