Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{28}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x- \frac{28}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{-28} & = & \color{red}{-33x} +6 \\\Leftrightarrow & 308x \color{red}{-28} \color{blue}{+28} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+28} \\\Leftrightarrow & 308x+33x& = & 6+28 \\\Leftrightarrow & \color{red}{341} x& = & 34 \\\Leftrightarrow & x = \frac{34}{341} & & \\ & V = \left\{ \frac{34}{341} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-270} & = & \color{red}{315x} +28 \\\Leftrightarrow & 756x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & 756x-315x& = & 28+270 \\\Leftrightarrow & \color{red}{441} x& = & 298 \\\Leftrightarrow & x = \frac{298}{441} & & \\ & V = \left\{ \frac{298}{441} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{4}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+4} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -90x \color{red}{+4} \color{blue}{-4} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-4} \\\Leftrightarrow & -90x+63x& = & 6-4 \\\Leftrightarrow & \color{red}{-27} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-27} & & \\\Leftrightarrow & x = \frac{-2}{27} & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -9x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{-90x} +9 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +9 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & 200x+90x& = & 9+24 \\\Leftrightarrow & \color{red}{290} x& = & 33 \\\Leftrightarrow & x = \frac{33}{290} & & \\ & V = \left\{ \frac{33}{290} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{24}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-168} & = & \color{red}{175x} +45 \\\Leftrightarrow & -420x \color{red}{-168} \color{blue}{+168} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{+168} \\\Leftrightarrow & -420x-175x& = & 45+168 \\\Leftrightarrow & \color{red}{-595} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-595} & & \\\Leftrightarrow & x = \frac{-213}{595} & & \\ & V = \left\{ \frac{-213}{595} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{4}{5}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-4} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -40x \color{red}{-4} \color{blue}{+4} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+4} \\\Leftrightarrow & -40x+15x& = & 4+4 \\\Leftrightarrow & \color{red}{-25} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-25} & & \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 4x+\frac{4}{7}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{-147x} +35 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{+147x} & = & \color{red}{-147x} +35 \color{blue}{+147x} \color{blue}{-12} \\\Leftrightarrow & 84x+147x& = & 35-12 \\\Leftrightarrow & \color{red}{231} x& = & 23 \\\Leftrightarrow & x = \frac{23}{231} & & \\ & V = \left\{ \frac{23}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{75x} +20 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -135x-75x& = & 20-36 \\\Leftrightarrow & \color{red}{-210} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-210} & & \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 28+18 \\\Leftrightarrow & \color{red}{-273} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-273} & & \\\Leftrightarrow & x = \frac{-46}{273} & & \\ & V = \left\{ \frac{-46}{273} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{12})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 21x+\frac{35}{12}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 12 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{+35} & = & \color{red}{24x} +10 \\\Leftrightarrow & 252x \color{red}{+35} \color{blue}{-35} \color{blue}{-24x} & = & \color{red}{24x} +10 \color{blue}{-24x} \color{blue}{-35} \\\Leftrightarrow & 252x-24x& = & 10-35 \\\Leftrightarrow & \color{red}{228} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{228} & & \\ & V = \left\{ \frac{-25}{228} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 792x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{561} x& = & 164 \\\Leftrightarrow & x = \frac{164}{561} & & \\ & V = \left\{ \frac{164}{561} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{2})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{25}{2}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{-125} & = & \color{red}{-40x} +12 \\\Leftrightarrow & -250x \color{red}{-125} \color{blue}{+125} \color{blue}{+40x} & = & \color{red}{-40x} +12 \color{blue}{+40x} \color{blue}{+125} \\\Leftrightarrow & -250x+40x& = & 12+125 \\\Leftrightarrow & \color{red}{-210} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-210} & & \\\Leftrightarrow & x = \frac{-137}{210} & & \\ & V = \left\{ \frac{-137}{210} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-01 16:08:52
Een site van Busleyden Atheneum Mechelen