Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{2})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -25x+\frac{25}{2}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x+ \frac{75}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{+75} & = & \color{red}{54x} +8 \\\Leftrightarrow & -150x \color{red}{+75} \color{blue}{-75} \color{blue}{-54x} & = & \color{red}{54x} +8 \color{blue}{-54x} \color{blue}{-75} \\\Leftrightarrow & -150x-54x& = & 8-75 \\\Leftrightarrow & \color{red}{-204} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-204} & & \\\Leftrightarrow & x = \frac{67}{204} & & \\ & V = \left\{ \frac{67}{204} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -18x+\frac{12}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-396}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -396x \color{red}{+24} & = & \color{red}{154x} +33 \\\Leftrightarrow & -396x \color{red}{+24} \color{blue}{-24} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-24} \\\Leftrightarrow & -396x-154x& = & 33-24 \\\Leftrightarrow & \color{red}{-550} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-550} & & \\\Leftrightarrow & x = \frac{-9}{550} & & \\ & V = \left\{ \frac{-9}{550} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+140} & = & \color{red}{539x} +110 \\\Leftrightarrow & 1540x \color{red}{+140} \color{blue}{-140} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-140} \\\Leftrightarrow & 1540x-539x& = & 110-140 \\\Leftrightarrow & \color{red}{1001} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{1001} & & \\ & V = \left\{ \frac{-30}{1001} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{385x} +20 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 495x-385x& = & 20+132 \\\Leftrightarrow & \color{red}{110} x& = & 152 \\\Leftrightarrow & x = \frac{152}{110} & & \\\Leftrightarrow & x = \frac{76}{55} & & \\ & V = \left\{ \frac{76}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{8})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{-231} & = & \color{red}{-352x} +16 \\\Leftrightarrow & -2464x \color{red}{-231} \color{blue}{+231} \color{blue}{+352x} & = & \color{red}{-352x} +16 \color{blue}{+352x} \color{blue}{+231} \\\Leftrightarrow & -2464x+352x& = & 16+231 \\\Leftrightarrow & \color{red}{-2112} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-2112} & & \\\Leftrightarrow & x = \frac{-247}{2112} & & \\ & V = \left\{ \frac{-247}{2112} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -30x+\frac{18}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+198} & = & \color{red}{385x} +25 \\\Leftrightarrow & -1650x \color{red}{+198} \color{blue}{-198} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{-198} \\\Leftrightarrow & -1650x-385x& = & 25-198 \\\Leftrightarrow & \color{red}{-2035} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-2035} & & \\\Leftrightarrow & x = \frac{173}{2035} & & \\ & V = \left\{ \frac{173}{2035} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{-140x} +36 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +36 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -400x+140x& = & 36+75 \\\Leftrightarrow & \color{red}{-260} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-260} & & \\\Leftrightarrow & x = \frac{-111}{260} & & \\ & V = \left\{ \frac{-111}{260} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-192}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -192x \color{red}{-80} & = & \color{red}{84x} +15 \\\Leftrightarrow & -192x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & -192x-84x& = & 15+80 \\\Leftrightarrow & \color{red}{-276} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-276} & & \\\Leftrightarrow & x = \frac{-95}{276} & & \\ & V = \left\{ \frac{-95}{276} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{12}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+12} & = & \color{red}{-55x} +6 \\\Leftrightarrow & 176x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & 176x+55x& = & 6-12 \\\Leftrightarrow & \color{red}{231} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{231} & & \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{11})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 8x+\frac{8}{11}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{880}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{550x} +77 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{-550x} & = & \color{red}{550x} +77 \color{blue}{-550x} \color{blue}{-80} \\\Leftrightarrow & 880x-550x& = & 77-80 \\\Leftrightarrow & \color{red}{330} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{330} & & \\\Leftrightarrow & x = \frac{-1}{110} & & \\ & V = \left\{ \frac{-1}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & -4x+\frac{5}{8} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -4x+\frac{5}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{-32x} +5 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{+32x} & = & \color{red}{-32x} +5 \color{blue}{+32x} \color{blue}{+21} \\\Leftrightarrow & -280x+32x& = & 5+21 \\\Leftrightarrow & \color{red}{-248} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-248} & & \\\Leftrightarrow & x = \frac{-13}{124} & & \\ & V = \left\{ \frac{-13}{124} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{7})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{+120} & = & \color{red}{-378x} +35 \\\Leftrightarrow & -840x \color{red}{+120} \color{blue}{-120} \color{blue}{+378x} & = & \color{red}{-378x} +35 \color{blue}{+378x} \color{blue}{-120} \\\Leftrightarrow & -840x+378x& = & 35-120 \\\Leftrightarrow & \color{red}{-462} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-462} & & \\\Leftrightarrow & x = \frac{85}{462} & & \\ & V = \left\{ \frac{85}{462} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-07 04:34:30
Een site van Busleyden Atheneum Mechelen