Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{7})& = & -9x+\frac{7}{11} \\\Leftrightarrow & 16x+\frac{8}{7}& = & -9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+88} & = & \color{red}{-693x} +49 \\\Leftrightarrow & 1232x \color{red}{+88} \color{blue}{-88} \color{blue}{+693x} & = & \color{red}{-693x} +49 \color{blue}{+693x} \color{blue}{-88} \\\Leftrightarrow & 1232x+693x& = & 49-88 \\\Leftrightarrow & \color{red}{1925} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{1925} & & \\ & V = \left\{ \frac{-39}{1925} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -9x+\frac{7}{9} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+42} & = & \color{red}{-81x} +7 \\\Leftrightarrow & 126x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +7 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & 126x+81x& = & 7-42 \\\Leftrightarrow & \color{red}{207} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{207} & & \\ & V = \left\{ \frac{-35}{207} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & -120x+25x& = & 6-24 \\\Leftrightarrow & \color{red}{-95} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-95} & & \\\Leftrightarrow & x = \frac{18}{95} & & \\ & V = \left\{ \frac{18}{95} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-330} & = & \color{red}{539x} +42 \\\Leftrightarrow & -2310x \color{red}{-330} \color{blue}{+330} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+330} \\\Leftrightarrow & -2310x-539x& = & 42+330 \\\Leftrightarrow & \color{red}{-2849} x& = & 372 \\\Leftrightarrow & x = \frac{372}{-2849} & & \\\Leftrightarrow & x = \frac{-372}{2849} & & \\ & V = \left\{ \frac{-372}{2849} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -4x-\frac{6}{5}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-240}{ \color{blue}{60} }x- \frac{72}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -240x \color{red}{-72} & = & \color{red}{300x} +25 \\\Leftrightarrow & -240x \color{red}{-72} \color{blue}{+72} \color{blue}{-300x} & = & \color{red}{300x} +25 \color{blue}{-300x} \color{blue}{+72} \\\Leftrightarrow & -240x-300x& = & 25+72 \\\Leftrightarrow & \color{red}{-540} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-540} & & \\\Leftrightarrow & x = \frac{-97}{540} & & \\ & V = \left\{ \frac{-97}{540} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 30x+\frac{18}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+198} & = & \color{red}{385x} +30 \\\Leftrightarrow & 1650x \color{red}{+198} \color{blue}{-198} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-198} \\\Leftrightarrow & 1650x-385x& = & 30-198 \\\Leftrightarrow & \color{red}{1265} x& = & -168 \\\Leftrightarrow & x = \frac{-168}{1265} & & \\ & V = \left\{ \frac{-168}{1265} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{11})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{20}{11}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1760}{ \color{blue}{88} }x+ \frac{160}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1760x \color{red}{+160} & = & \color{red}{-264x} +77 \\\Leftrightarrow & -1760x \color{red}{+160} \color{blue}{-160} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{-160} \\\Leftrightarrow & -1760x+264x& = & 77-160 \\\Leftrightarrow & \color{red}{-1496} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-1496} & & \\\Leftrightarrow & x = \frac{83}{1496} & & \\ & V = \left\{ \frac{83}{1496} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{-24} & = & \color{red}{70x} +35 \\\Leftrightarrow & -160x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & -160x-70x& = & 35+24 \\\Leftrightarrow & \color{red}{-230} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-230} & & \\\Leftrightarrow & x = \frac{-59}{230} & & \\ & V = \left\{ \frac{-59}{230} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{10}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-30} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 132x \color{red}{-30} \color{blue}{+30} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+30} \\\Leftrightarrow & 132x+165x& = & 110+30 \\\Leftrightarrow & \color{red}{297} x& = & 140 \\\Leftrightarrow & x = \frac{140}{297} & & \\ & V = \left\{ \frac{140}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{7})& = & -9x+\frac{3}{5} \\\Leftrightarrow & 8x-\frac{8}{7}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{-315x} +21 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +21 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & 280x+315x& = & 21+40 \\\Leftrightarrow & \color{red}{595} x& = & 61 \\\Leftrightarrow & x = \frac{61}{595} & & \\ & V = \left\{ \frac{61}{595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -240x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{-345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-345} & & \\\Leftrightarrow & x = \frac{26}{345} & & \\ & V = \left\{ \frac{26}{345} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{9}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-9} & = & \color{red}{35x} +6 \\\Leftrightarrow & -30x \color{red}{-9} \color{blue}{+9} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+9} \\\Leftrightarrow & -30x-35x& = & 6+9 \\\Leftrightarrow & \color{red}{-65} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-65} & & \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-24 17:50:16
Een site van Busleyden Atheneum Mechelen