Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{245x} +28 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & -350x-245x& = & 28+50 \\\Leftrightarrow & \color{red}{-595} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-595} & & \\\Leftrightarrow & x = \frac{-78}{595} & & \\ & V = \left\{ \frac{-78}{595} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{140x} +36 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +36 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -252x-140x& = & 36+105 \\\Leftrightarrow & \color{red}{-392} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-392} & & \\\Leftrightarrow & x = \frac{-141}{392} & & \\ & V = \left\{ \frac{-141}{392} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & -7x+\frac{9}{8} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-192} & = & \color{red}{-280x} +45 \\\Leftrightarrow & 1200x \color{red}{-192} \color{blue}{+192} \color{blue}{+280x} & = & \color{red}{-280x} +45 \color{blue}{+280x} \color{blue}{+192} \\\Leftrightarrow & 1200x+280x& = & 45+192 \\\Leftrightarrow & \color{red}{1480} x& = & 237 \\\Leftrightarrow & x = \frac{237}{1480} & & \\ & V = \left\{ \frac{237}{1480} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{+162} & = & \color{red}{495x} +44 \\\Leftrightarrow & 2376x \color{red}{+162} \color{blue}{-162} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{-162} \\\Leftrightarrow & 2376x-495x& = & 44-162 \\\Leftrightarrow & \color{red}{1881} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{1881} & & \\ & V = \left\{ \frac{-118}{1881} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{8}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+80} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1320x \color{red}{+80} \color{blue}{-80} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-80} \\\Leftrightarrow & 1320x-550x& = & 99-80 \\\Leftrightarrow & \color{red}{770} x& = & 19 \\\Leftrightarrow & x = \frac{19}{770} & & \\ & V = \left\{ \frac{19}{770} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{9})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -35x+\frac{28}{9}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1575}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1575x \color{red}{+140} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -1575x \color{red}{+140} \color{blue}{-140} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-140} \\\Leftrightarrow & -1575x+135x& = & 18-140 \\\Leftrightarrow & \color{red}{-1440} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-1440} & & \\\Leftrightarrow & x = \frac{61}{720} & & \\ & V = \left\{ \frac{61}{720} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{3})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -25x+\frac{25}{3}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+275} & = & \color{red}{297x} +30 \\\Leftrightarrow & -825x \color{red}{+275} \color{blue}{-275} \color{blue}{-297x} & = & \color{red}{297x} +30 \color{blue}{-297x} \color{blue}{-275} \\\Leftrightarrow & -825x-297x& = & 30-275 \\\Leftrightarrow & \color{red}{-1122} x& = & -245 \\\Leftrightarrow & x = \frac{-245}{-1122} & & \\\Leftrightarrow & x = \frac{245}{1122} & & \\ & V = \left\{ \frac{245}{1122} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{352x} +40 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{-352x} & = & \color{red}{352x} +40 \color{blue}{-352x} \color{blue}{-165} \\\Leftrightarrow & -660x-352x& = & 40-165 \\\Leftrightarrow & \color{red}{-1012} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1012} & & \\\Leftrightarrow & x = \frac{125}{1012} & & \\ & V = \left\{ \frac{125}{1012} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-132} & = & \color{red}{385x} +50 \\\Leftrightarrow & -880x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -880x-385x& = & 50+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 182 \\\Leftrightarrow & x = \frac{182}{-1265} & & \\\Leftrightarrow & x = \frac{-182}{1265} & & \\ & V = \left\{ \frac{-182}{1265} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{3})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 28x-\frac{35}{3}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-245} & = & \color{red}{63x} +24 \\\Leftrightarrow & 588x \color{red}{-245} \color{blue}{+245} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{+245} \\\Leftrightarrow & 588x-63x& = & 24+245 \\\Leftrightarrow & \color{red}{525} x& = & 269 \\\Leftrightarrow & x = \frac{269}{525} & & \\ & V = \left\{ \frac{269}{525} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-110} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -330x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -330x+231x& = & 15+110 \\\Leftrightarrow & \color{red}{-99} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-99} & & \\\Leftrightarrow & x = \frac{-125}{99} & & \\ & V = \left\{ \frac{-125}{99} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 18x+\frac{24}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{504}{ \color{blue}{28} }x+ \frac{96}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 504x \color{red}{+96} & = & \color{red}{196x} +21 \\\Leftrightarrow & 504x \color{red}{+96} \color{blue}{-96} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-96} \\\Leftrightarrow & 504x-196x& = & 21-96 \\\Leftrightarrow & \color{red}{308} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{308} & & \\ & V = \left\{ \frac{-75}{308} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-31 01:32:06
Een site van Busleyden Atheneum Mechelen