Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{3})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{48x} +21 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{-48x} & = & \color{red}{48x} +21 \color{blue}{-48x} \color{blue}{-40} \\\Leftrightarrow & -90x-48x& = & 21-40 \\\Leftrightarrow & \color{red}{-138} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-138} & & \\\Leftrightarrow & x = \frac{19}{138} & & \\ & V = \left\{ \frac{19}{138} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{3})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 8x+\frac{20}{3}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+220} & = & \color{red}{-99x} +21 \\\Leftrightarrow & 264x \color{red}{+220} \color{blue}{-220} \color{blue}{+99x} & = & \color{red}{-99x} +21 \color{blue}{+99x} \color{blue}{-220} \\\Leftrightarrow & 264x+99x& = & 21-220 \\\Leftrightarrow & \color{red}{363} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{363} & & \\ & V = \left\{ \frac{-199}{363} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{-15} & = & \color{red}{-20x} +6 \\\Leftrightarrow & -36x \color{red}{-15} \color{blue}{+15} \color{blue}{+20x} & = & \color{red}{-20x} +6 \color{blue}{+20x} \color{blue}{+15} \\\Leftrightarrow & -36x+20x& = & 6+15 \\\Leftrightarrow & \color{red}{-16} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-16} & & \\\Leftrightarrow & x = \frac{-21}{16} & & \\ & V = \left\{ \frac{-21}{16} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+88} & = & \color{red}{-495x} +54 \\\Leftrightarrow & 792x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & 792x+495x& = & 54-88 \\\Leftrightarrow & \color{red}{1287} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{1287} & & \\ & V = \left\{ \frac{-34}{1287} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+120} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -336x \color{red}{+120} \color{blue}{-120} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-120} \\\Leftrightarrow & -336x+140x& = & 63-120 \\\Leftrightarrow & \color{red}{-196} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-196} & & \\\Leftrightarrow & x = \frac{57}{196} & & \\ & V = \left\{ \frac{57}{196} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{+45} & = & \color{red}{84x} +5 \\\Leftrightarrow & -108x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +5 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & -108x-84x& = & 5-45 \\\Leftrightarrow & \color{red}{-192} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-192} & & \\\Leftrightarrow & x = \frac{5}{24} & & \\ & V = \left\{ \frac{5}{24} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+30} \\\Leftrightarrow & -210x+147x& = & 56+30 \\\Leftrightarrow & \color{red}{-63} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-63} & & \\\Leftrightarrow & x = \frac{-86}{63} & & \\ & V = \left\{ \frac{-86}{63} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 6x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{144x} +64 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{-144x} & = & \color{red}{144x} +64 \color{blue}{-144x} \color{blue}{+63} \\\Leftrightarrow & -840x-144x& = & 64+63 \\\Leftrightarrow & \color{red}{-984} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-984} & & \\\Leftrightarrow & x = \frac{-127}{984} & & \\ & V = \left\{ \frac{-127}{984} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{2})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -10x-\frac{15}{2}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-165} & = & \color{red}{-154x} +8 \\\Leftrightarrow & -220x \color{red}{-165} \color{blue}{+165} \color{blue}{+154x} & = & \color{red}{-154x} +8 \color{blue}{+154x} \color{blue}{+165} \\\Leftrightarrow & -220x+154x& = & 8+165 \\\Leftrightarrow & \color{red}{-66} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-66} & & \\\Leftrightarrow & x = \frac{-173}{66} & & \\ & V = \left\{ \frac{-173}{66} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{11})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{15}{11}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x+ \frac{135}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{+135} & = & \color{red}{-792x} +44 \\\Leftrightarrow & -1485x \color{red}{+135} \color{blue}{-135} \color{blue}{+792x} & = & \color{red}{-792x} +44 \color{blue}{+792x} \color{blue}{-135} \\\Leftrightarrow & -1485x+792x& = & 44-135 \\\Leftrightarrow & \color{red}{-693} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{-693} & & \\\Leftrightarrow & x = \frac{13}{99} & & \\ & V = \left\{ \frac{13}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x+ \frac{50}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{+50} & = & \color{red}{28x} +7 \\\Leftrightarrow & -40x \color{red}{+50} \color{blue}{-50} \color{blue}{-28x} & = & \color{red}{28x} +7 \color{blue}{-28x} \color{blue}{-50} \\\Leftrightarrow & -40x-28x& = & 7-50 \\\Leftrightarrow & \color{red}{-68} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-68} & & \\\Leftrightarrow & x = \frac{43}{68} & & \\ & V = \left\{ \frac{43}{68} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & -4x+\frac{7}{3} \\\Leftrightarrow & 15x-\frac{9}{2}& = & -4x+\frac{7}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{27}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-27} & = & \color{red}{-24x} +14 \\\Leftrightarrow & 90x \color{red}{-27} \color{blue}{+27} \color{blue}{+24x} & = & \color{red}{-24x} +14 \color{blue}{+24x} \color{blue}{+27} \\\Leftrightarrow & 90x+24x& = & 14+27 \\\Leftrightarrow & \color{red}{114} x& = & 41 \\\Leftrightarrow & x = \frac{41}{114} & & \\ & V = \left\{ \frac{41}{114} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-31 01:57:18
Een site van Busleyden Atheneum Mechelen