Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+12} & = & \color{red}{-126x} +21 \\\Leftrightarrow & 140x \color{red}{+12} \color{blue}{-12} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-12} \\\Leftrightarrow & 140x+126x& = & 21-12 \\\Leftrightarrow & \color{red}{266} x& = & 9 \\\Leftrightarrow & x = \frac{9}{266} & & \\ & V = \left\{ \frac{9}{266} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-48} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{-48} \color{blue}{+48} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+48} \\\Leftrightarrow & 252x-105x& = & 14+48 \\\Leftrightarrow & \color{red}{147} x& = & 62 \\\Leftrightarrow & x = \frac{62}{147} & & \\ & V = \left\{ \frac{62}{147} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{11})& = & 5x+\frac{7}{9} \\\Leftrightarrow & -28x-\frac{14}{11}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{126}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-126} & = & \color{red}{495x} +77 \\\Leftrightarrow & -2772x \color{red}{-126} \color{blue}{+126} \color{blue}{-495x} & = & \color{red}{495x} +77 \color{blue}{-495x} \color{blue}{+126} \\\Leftrightarrow & -2772x-495x& = & 77+126 \\\Leftrightarrow & \color{red}{-3267} x& = & 203 \\\Leftrightarrow & x = \frac{203}{-3267} & & \\\Leftrightarrow & x = \frac{-203}{3267} & & \\ & V = \left\{ \frac{-203}{3267} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 20x+\frac{25}{8}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+25} & = & \color{red}{-72x} +5 \\\Leftrightarrow & 160x \color{red}{+25} \color{blue}{-25} \color{blue}{+72x} & = & \color{red}{-72x} +5 \color{blue}{+72x} \color{blue}{-25} \\\Leftrightarrow & 160x+72x& = & 5-25 \\\Leftrightarrow & \color{red}{232} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{232} & & \\\Leftrightarrow & x = \frac{-5}{58} & & \\ & V = \left\{ \frac{-5}{58} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -2x+\frac{9}{2} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-28} & = & \color{red}{-12x} +27 \\\Leftrightarrow & -168x \color{red}{-28} \color{blue}{+28} \color{blue}{+12x} & = & \color{red}{-12x} +27 \color{blue}{+12x} \color{blue}{+28} \\\Leftrightarrow & -168x+12x& = & 27+28 \\\Leftrightarrow & \color{red}{-156} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-156} & & \\\Leftrightarrow & x = \frac{-55}{156} & & \\ & V = \left\{ \frac{-55}{156} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{+216} & = & \color{red}{-495x} +44 \\\Leftrightarrow & 2376x \color{red}{+216} \color{blue}{-216} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-216} \\\Leftrightarrow & 2376x+495x& = & 44-216 \\\Leftrightarrow & \color{red}{2871} x& = & -172 \\\Leftrightarrow & x = \frac{-172}{2871} & & \\ & V = \left\{ \frac{-172}{2871} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+60} & = & \color{red}{63x} +4 \\\Leftrightarrow & 180x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & 180x-63x& = & 4-60 \\\Leftrightarrow & \color{red}{117} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{117} & & \\ & V = \left\{ \frac{-56}{117} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{70x} +15 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-48} \\\Leftrightarrow & -300x-70x& = & 15-48 \\\Leftrightarrow & \color{red}{-370} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-370} & & \\\Leftrightarrow & x = \frac{33}{370} & & \\ & V = \left\{ \frac{33}{370} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-44} & = & \color{red}{385x} +25 \\\Leftrightarrow & 220x \color{red}{-44} \color{blue}{+44} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{+44} \\\Leftrightarrow & 220x-385x& = & 25+44 \\\Leftrightarrow & \color{red}{-165} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-165} & & \\\Leftrightarrow & x = \frac{-23}{55} & & \\ & V = \left\{ \frac{-23}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{30x} +35 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{-30x} & = & \color{red}{30x} +35 \color{blue}{-30x} \color{blue}{+24} \\\Leftrightarrow & 200x-30x& = & 35+24 \\\Leftrightarrow & \color{red}{170} x& = & 59 \\\Leftrightarrow & x = \frac{59}{170} & & \\ & V = \left\{ \frac{59}{170} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{12})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{25}{12}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-600}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -600x \color{red}{-125} & = & \color{red}{420x} +72 \\\Leftrightarrow & -600x \color{red}{-125} \color{blue}{+125} \color{blue}{-420x} & = & \color{red}{420x} +72 \color{blue}{-420x} \color{blue}{+125} \\\Leftrightarrow & -600x-420x& = & 72+125 \\\Leftrightarrow & \color{red}{-1020} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1020} & & \\\Leftrightarrow & x = \frac{-197}{1020} & & \\ & V = \left\{ \frac{-197}{1020} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{15}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+75} & = & \color{red}{245x} +42 \\\Leftrightarrow & 700x \color{red}{+75} \color{blue}{-75} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-75} \\\Leftrightarrow & 700x-245x& = & 42-75 \\\Leftrightarrow & \color{red}{455} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{455} & & \\ & V = \left\{ \frac{-33}{455} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-21 18:53:35
Een site van Busleyden Atheneum Mechelen