Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{3})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 6x+\frac{4}{3}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+20} & = & \color{red}{-105x} +12 \\\Leftrightarrow & 90x \color{red}{+20} \color{blue}{-20} \color{blue}{+105x} & = & \color{red}{-105x} +12 \color{blue}{+105x} \color{blue}{-20} \\\Leftrightarrow & 90x+105x& = & 12-20 \\\Leftrightarrow & \color{red}{195} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{195} & & \\ & V = \left\{ \frac{-8}{195} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{45x} +40 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 150x-45x& = & 40-12 \\\Leftrightarrow & \color{red}{105} x& = & 28 \\\Leftrightarrow & x = \frac{28}{105} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{11})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+162} & = & \color{red}{-495x} +77 \\\Leftrightarrow & -1188x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +77 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & -1188x+495x& = & 77-162 \\\Leftrightarrow & \color{red}{-693} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-693} & & \\\Leftrightarrow & x = \frac{85}{693} & & \\ & V = \left\{ \frac{85}{693} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{15}{4}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{-252x} +40 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{+252x} & = & \color{red}{-252x} +40 \color{blue}{+252x} \color{blue}{+105} \\\Leftrightarrow & 560x+252x& = & 40+105 \\\Leftrightarrow & \color{red}{812} x& = & 145 \\\Leftrightarrow & x = \frac{145}{812} & & \\\Leftrightarrow & x = \frac{5}{28} & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{11})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{21}{11}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+63} & = & \color{red}{-99x} +110 \\\Leftrightarrow & -462x \color{red}{+63} \color{blue}{-63} \color{blue}{+99x} & = & \color{red}{-99x} +110 \color{blue}{+99x} \color{blue}{-63} \\\Leftrightarrow & -462x+99x& = & 110-63 \\\Leftrightarrow & \color{red}{-363} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-363} & & \\\Leftrightarrow & x = \frac{-47}{363} & & \\ & V = \left\{ \frac{-47}{363} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{15}{8}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{400}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{-280x} +32 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{+280x} & = & \color{red}{-280x} +32 \color{blue}{+280x} \color{blue}{-75} \\\Leftrightarrow & 400x+280x& = & 32-75 \\\Leftrightarrow & \color{red}{680} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{680} & & \\ & V = \left\{ \frac{-43}{680} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-330} & = & \color{red}{539x} +70 \\\Leftrightarrow & -2310x \color{red}{-330} \color{blue}{+330} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{+330} \\\Leftrightarrow & -2310x-539x& = & 70+330 \\\Leftrightarrow & \color{red}{-2849} x& = & 400 \\\Leftrightarrow & x = \frac{400}{-2849} & & \\\Leftrightarrow & x = \frac{-400}{2849} & & \\ & V = \left\{ \frac{-400}{2849} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{-165} & = & \color{red}{792x} +48 \\\Leftrightarrow & 1760x \color{red}{-165} \color{blue}{+165} \color{blue}{-792x} & = & \color{red}{792x} +48 \color{blue}{-792x} \color{blue}{+165} \\\Leftrightarrow & 1760x-792x& = & 48+165 \\\Leftrightarrow & \color{red}{968} x& = & 213 \\\Leftrightarrow & x = \frac{213}{968} & & \\ & V = \left\{ \frac{213}{968} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+30} & = & \color{red}{275x} +66 \\\Leftrightarrow & -495x \color{red}{+30} \color{blue}{-30} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-30} \\\Leftrightarrow & -495x-275x& = & 66-30 \\\Leftrightarrow & \color{red}{-770} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-770} & & \\\Leftrightarrow & x = \frac{-18}{385} & & \\ & V = \left\{ \frac{-18}{385} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+270} & = & \color{red}{441x} +14 \\\Leftrightarrow & 756x \color{red}{+270} \color{blue}{-270} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{-270} \\\Leftrightarrow & 756x-441x& = & 14-270 \\\Leftrightarrow & \color{red}{315} x& = & -256 \\\Leftrightarrow & x = \frac{-256}{315} & & \\ & V = \left\{ \frac{-256}{315} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{140x} +8 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +8 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -336x-140x& = & 8+105 \\\Leftrightarrow & \color{red}{-476} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-476} & & \\\Leftrightarrow & x = \frac{-113}{476} & & \\ & V = \left\{ \frac{-113}{476} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-07 17:47:05
Een site van Busleyden Atheneum Mechelen