Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-220} & = & \color{red}{-693x} +54 \\\Leftrightarrow & -1584x \color{red}{-220} \color{blue}{+220} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{+220} \\\Leftrightarrow & -1584x+693x& = & 54+220 \\\Leftrightarrow & \color{red}{-891} x& = & 274 \\\Leftrightarrow & x = \frac{274}{-891} & & \\\Leftrightarrow & x = \frac{-274}{891} & & \\ & V = \left\{ \frac{-274}{891} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-14} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 84x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & 84x+15x& = & 8+14 \\\Leftrightarrow & \color{red}{99} x& = & 22 \\\Leftrightarrow & x = \frac{22}{99} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & -4x+\frac{5}{2} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -4x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{-40} & = & \color{red}{-24x} +15 \\\Leftrightarrow & 150x \color{red}{-40} \color{blue}{+40} \color{blue}{+24x} & = & \color{red}{-24x} +15 \color{blue}{+24x} \color{blue}{+40} \\\Leftrightarrow & 150x+24x& = & 15+40 \\\Leftrightarrow & \color{red}{174} x& = & 55 \\\Leftrightarrow & x = \frac{55}{174} & & \\ & V = \left\{ \frac{55}{174} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{4})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 14x+\frac{35}{4}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{280}{ \color{blue}{20} }x+ \frac{175}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 280x \color{red}{+175} & = & \color{red}{-100x} +24 \\\Leftrightarrow & 280x \color{red}{+175} \color{blue}{-175} \color{blue}{+100x} & = & \color{red}{-100x} +24 \color{blue}{+100x} \color{blue}{-175} \\\Leftrightarrow & 280x+100x& = & 24-175 \\\Leftrightarrow & \color{red}{380} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{380} & & \\ & V = \left\{ \frac{-151}{380} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{2})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{25}{2}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+225} & = & \color{red}{-126x} +16 \\\Leftrightarrow & -180x \color{red}{+225} \color{blue}{-225} \color{blue}{+126x} & = & \color{red}{-126x} +16 \color{blue}{+126x} \color{blue}{-225} \\\Leftrightarrow & -180x+126x& = & 16-225 \\\Leftrightarrow & \color{red}{-54} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{-54} & & \\\Leftrightarrow & x = \frac{209}{54} & & \\ & V = \left\{ \frac{209}{54} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{225x} +40 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -540x-225x& = & 40-108 \\\Leftrightarrow & \color{red}{-765} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-765} & & \\\Leftrightarrow & x = \frac{4}{45} & & \\ & V = \left\{ \frac{4}{45} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{3})& = & 2x+\frac{10}{7} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-196} & = & \color{red}{42x} +30 \\\Leftrightarrow & -588x \color{red}{-196} \color{blue}{+196} \color{blue}{-42x} & = & \color{red}{42x} +30 \color{blue}{-42x} \color{blue}{+196} \\\Leftrightarrow & -588x-42x& = & 30+196 \\\Leftrightarrow & \color{red}{-630} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-630} & & \\\Leftrightarrow & x = \frac{-113}{315} & & \\ & V = \left\{ \frac{-113}{315} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{9}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-45} & = & \color{red}{245x} +14 \\\Leftrightarrow & -210x \color{red}{-45} \color{blue}{+45} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{+45} \\\Leftrightarrow & -210x-245x& = & 14+45 \\\Leftrightarrow & \color{red}{-455} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-455} & & \\\Leftrightarrow & x = \frac{-59}{455} & & \\ & V = \left\{ \frac{-59}{455} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-12} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 220x \color{red}{-12} \color{blue}{+12} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+12} \\\Leftrightarrow & 220x+154x& = & 77+12 \\\Leftrightarrow & \color{red}{374} x& = & 89 \\\Leftrightarrow & x = \frac{89}{374} & & \\ & V = \left\{ \frac{89}{374} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{-66} & = & \color{red}{385x} +42 \\\Leftrightarrow & -693x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -693x-385x& = & 42+66 \\\Leftrightarrow & \color{red}{-1078} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-1078} & & \\\Leftrightarrow & x = \frac{-54}{539} & & \\ & V = \left\{ \frac{-54}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-30} & = & \color{red}{189x} +70 \\\Leftrightarrow & 420x \color{red}{-30} \color{blue}{+30} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{+30} \\\Leftrightarrow & 420x-189x& = & 70+30 \\\Leftrightarrow & \color{red}{231} x& = & 100 \\\Leftrightarrow & x = \frac{100}{231} & & \\ & V = \left\{ \frac{100}{231} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{3})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+100} & = & \color{red}{75x} +18 \\\Leftrightarrow & -180x \color{red}{+100} \color{blue}{-100} \color{blue}{-75x} & = & \color{red}{75x} +18 \color{blue}{-75x} \color{blue}{-100} \\\Leftrightarrow & -180x-75x& = & 18-100 \\\Leftrightarrow & \color{red}{-255} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-255} & & \\\Leftrightarrow & x = \frac{82}{255} & & \\ & V = \left\{ \frac{82}{255} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-26 05:56:22
Een site van Busleyden Atheneum Mechelen