Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{792}{ \color{blue}{66} }x+ \frac{108}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 792x \color{red}{+108} & = & \color{red}{-462x} +77 \\\Leftrightarrow & 792x \color{red}{+108} \color{blue}{-108} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{-108} \\\Leftrightarrow & 792x+462x& = & 77-108 \\\Leftrightarrow & \color{red}{1254} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{1254} & & \\ & V = \left\{ \frac{-31}{1254} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{385x} +42 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1848x-385x& = & 42+330 \\\Leftrightarrow & \color{red}{1463} x& = & 372 \\\Leftrightarrow & x = \frac{372}{1463} & & \\ & V = \left\{ \frac{372}{1463} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{8})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{-165} & = & \color{red}{440x} +40 \\\Leftrightarrow & 1056x \color{red}{-165} \color{blue}{+165} \color{blue}{-440x} & = & \color{red}{440x} +40 \color{blue}{-440x} \color{blue}{+165} \\\Leftrightarrow & 1056x-440x& = & 40+165 \\\Leftrightarrow & \color{red}{616} x& = & 205 \\\Leftrightarrow & x = \frac{205}{616} & & \\ & V = \left\{ \frac{205}{616} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 18x-\frac{12}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1188}{ \color{blue}{66} }x- \frac{72}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1188x \color{red}{-72} & = & \color{red}{330x} +55 \\\Leftrightarrow & 1188x \color{red}{-72} \color{blue}{+72} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{+72} \\\Leftrightarrow & 1188x-330x& = & 55+72 \\\Leftrightarrow & \color{red}{858} x& = & 127 \\\Leftrightarrow & x = \frac{127}{858} & & \\ & V = \left\{ \frac{127}{858} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+72} & = & \color{red}{-75x} +50 \\\Leftrightarrow & -360x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -360x+75x& = & 50-72 \\\Leftrightarrow & \color{red}{-285} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-285} & & \\\Leftrightarrow & x = \frac{22}{285} & & \\ & V = \left\{ \frac{22}{285} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-120}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -120x \color{red}{-80} & = & \color{red}{-150x} +27 \\\Leftrightarrow & -120x \color{red}{-80} \color{blue}{+80} \color{blue}{+150x} & = & \color{red}{-150x} +27 \color{blue}{+150x} \color{blue}{+80} \\\Leftrightarrow & -120x+150x& = & 27+80 \\\Leftrightarrow & \color{red}{30} x& = & 107 \\\Leftrightarrow & x = \frac{107}{30} & & \\ & V = \left\{ \frac{107}{30} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{4})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{-84x} +28 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & 180x+84x& = & 28-45 \\\Leftrightarrow & \color{red}{264} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{264} & & \\ & V = \left\{ \frac{-17}{264} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{-140x} +18 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +18 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & 300x+140x& = & 18+75 \\\Leftrightarrow & \color{red}{440} x& = & 93 \\\Leftrightarrow & x = \frac{93}{440} & & \\ & V = \left\{ \frac{93}{440} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{+84} & = & \color{red}{105x} +45 \\\Leftrightarrow & 560x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 560x-105x& = & 45-84 \\\Leftrightarrow & \color{red}{455} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{455} & & \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{12x} +4 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{-12x} & = & \color{red}{12x} +4 \color{blue}{-12x} \color{blue}{+14} \\\Leftrightarrow & -105x-12x& = & 4+14 \\\Leftrightarrow & \color{red}{-117} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-117} & & \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+80} & = & \color{red}{315x} +42 \\\Leftrightarrow & -280x \color{red}{+80} \color{blue}{-80} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{-80} \\\Leftrightarrow & -280x-315x& = & 42-80 \\\Leftrightarrow & \color{red}{-595} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-595} & & \\\Leftrightarrow & x = \frac{38}{595} & & \\ & V = \left\{ \frac{38}{595} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-90} \\\Leftrightarrow & 990x+231x& = & 44-90 \\\Leftrightarrow & \color{red}{1221} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{1221} & & \\ & V = \left\{ \frac{-46}{1221} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-07 01:31:05
Een site van Busleyden Atheneum Mechelen