Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{9})& = & -4x+\frac{9}{7} \\\Leftrightarrow & 35x+\frac{35}{9}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{2205}{ \color{blue}{63} }x+ \frac{245}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 2205x \color{red}{+245} & = & \color{red}{-252x} +81 \\\Leftrightarrow & 2205x \color{red}{+245} \color{blue}{-245} \color{blue}{+252x} & = & \color{red}{-252x} +81 \color{blue}{+252x} \color{blue}{-245} \\\Leftrightarrow & 2205x+252x& = & 81-245 \\\Leftrightarrow & \color{red}{2457} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{2457} & & \\ & V = \left\{ \frac{-164}{2457} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+20} & = & \color{red}{98x} +35 \\\Leftrightarrow & 56x \color{red}{+20} \color{blue}{-20} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{-20} \\\Leftrightarrow & 56x-98x& = & 35-20 \\\Leftrightarrow & \color{red}{-42} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-42} & & \\\Leftrightarrow & x = \frac{-5}{14} & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{-180} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -3300x \color{red}{-180} \color{blue}{+180} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{+180} \\\Leftrightarrow & -3300x+770x& = & 33+180 \\\Leftrightarrow & \color{red}{-2530} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-2530} & & \\\Leftrightarrow & x = \frac{-213}{2530} & & \\ & V = \left\{ \frac{-213}{2530} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & 9x+\frac{7}{6} \\\Leftrightarrow & -4x-\frac{4}{9}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{162x} +21 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{-162x} & = & \color{red}{162x} +21 \color{blue}{-162x} \color{blue}{+8} \\\Leftrightarrow & -72x-162x& = & 21+8 \\\Leftrightarrow & \color{red}{-234} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-234} & & \\\Leftrightarrow & x = \frac{-29}{234} & & \\ & V = \left\{ \frac{-29}{234} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x-\frac{8}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-80} & = & \color{red}{490x} +63 \\\Leftrightarrow & -420x \color{red}{-80} \color{blue}{+80} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+80} \\\Leftrightarrow & -420x-490x& = & 63+80 \\\Leftrightarrow & \color{red}{-910} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-910} & & \\\Leftrightarrow & x = \frac{-11}{70} & & \\ & V = \left\{ \frac{-11}{70} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{70x} +35 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 150x-70x& = & 35-24 \\\Leftrightarrow & \color{red}{80} x& = & 11 \\\Leftrightarrow & x = \frac{11}{80} & & \\ & V = \left\{ \frac{11}{80} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{8})& = & 8x+\frac{2}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{448x} +16 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{-448x} & = & \color{red}{448x} +16 \color{blue}{-448x} \color{blue}{+147} \\\Leftrightarrow & 1176x-448x& = & 16+147 \\\Leftrightarrow & \color{red}{728} x& = & 163 \\\Leftrightarrow & x = \frac{163}{728} & & \\ & V = \left\{ \frac{163}{728} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{+144} & = & \color{red}{616x} +99 \\\Leftrightarrow & -2640x \color{red}{+144} \color{blue}{-144} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{-144} \\\Leftrightarrow & -2640x-616x& = & 99-144 \\\Leftrightarrow & \color{red}{-3256} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-3256} & & \\\Leftrightarrow & x = \frac{45}{3256} & & \\ & V = \left\{ \frac{45}{3256} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x-\frac{21}{11}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-63} & = & \color{red}{264x} +44 \\\Leftrightarrow & -693x \color{red}{-63} \color{blue}{+63} \color{blue}{-264x} & = & \color{red}{264x} +44 \color{blue}{-264x} \color{blue}{+63} \\\Leftrightarrow & -693x-264x& = & 44+63 \\\Leftrightarrow & \color{red}{-957} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-957} & & \\\Leftrightarrow & x = \frac{-107}{957} & & \\ & V = \left\{ \frac{-107}{957} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{50x} +3 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{+36} \\\Leftrightarrow & -240x-50x& = & 3+36 \\\Leftrightarrow & \color{red}{-290} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-290} & & \\\Leftrightarrow & x = \frac{-39}{290} & & \\ & V = \left\{ \frac{-39}{290} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{120x} +25 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{-120x} & = & \color{red}{120x} +25 \color{blue}{-120x} \color{blue}{-72} \\\Leftrightarrow & -450x-120x& = & 25-72 \\\Leftrightarrow & \color{red}{-570} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-570} & & \\\Leftrightarrow & x = \frac{47}{570} & & \\ & V = \left\{ \frac{47}{570} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{-162x} +20 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{+162x} & = & \color{red}{-162x} +20 \color{blue}{+162x} \color{blue}{-105} \\\Leftrightarrow & 252x+162x& = & 20-105 \\\Leftrightarrow & \color{red}{414} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{414} & & \\ & V = \left\{ \frac{-85}{414} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-14 23:49:20
Een site van Busleyden Atheneum Mechelen