Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+36} \\\Leftrightarrow & -528x+231x& = & 110+36 \\\Leftrightarrow & \color{red}{-297} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-297} & & \\\Leftrightarrow & x = \frac{-146}{297} & & \\ & V = \left\{ \frac{-146}{297} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{-308} & = & \color{red}{-495x} +54 \\\Leftrightarrow & -1386x \color{red}{-308} \color{blue}{+308} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{+308} \\\Leftrightarrow & -1386x+495x& = & 54+308 \\\Leftrightarrow & \color{red}{-891} x& = & 362 \\\Leftrightarrow & x = \frac{362}{-891} & & \\\Leftrightarrow & x = \frac{-362}{891} & & \\ & V = \left\{ \frac{-362}{891} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-154} \\\Leftrightarrow & 924x+297x& = & 18-154 \\\Leftrightarrow & \color{red}{1221} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{1221} & & \\ & V = \left\{ \frac{-136}{1221} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+88} & = & \color{red}{165x} +6 \\\Leftrightarrow & -132x \color{red}{+88} \color{blue}{-88} \color{blue}{-165x} & = & \color{red}{165x} +6 \color{blue}{-165x} \color{blue}{-88} \\\Leftrightarrow & -132x-165x& = & 6-88 \\\Leftrightarrow & \color{red}{-297} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-297} & & \\\Leftrightarrow & x = \frac{82}{297} & & \\ & V = \left\{ \frac{82}{297} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{+80} & = & \color{red}{-616x} +77 \\\Leftrightarrow & -880x \color{red}{+80} \color{blue}{-80} \color{blue}{+616x} & = & \color{red}{-616x} +77 \color{blue}{+616x} \color{blue}{-80} \\\Leftrightarrow & -880x+616x& = & 77-80 \\\Leftrightarrow & \color{red}{-264} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-264} & & \\\Leftrightarrow & x = \frac{1}{88} & & \\ & V = \left\{ \frac{1}{88} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{2})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{21}{2}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+63} & = & \color{red}{-30x} +8 \\\Leftrightarrow & 84x \color{red}{+63} \color{blue}{-63} \color{blue}{+30x} & = & \color{red}{-30x} +8 \color{blue}{+30x} \color{blue}{-63} \\\Leftrightarrow & 84x+30x& = & 8-63 \\\Leftrightarrow & \color{red}{114} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{114} & & \\ & V = \left\{ \frac{-55}{114} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-48}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -48x \color{red}{+30} & = & \color{red}{56x} +3 \\\Leftrightarrow & -48x \color{red}{+30} \color{blue}{-30} \color{blue}{-56x} & = & \color{red}{56x} +3 \color{blue}{-56x} \color{blue}{-30} \\\Leftrightarrow & -48x-56x& = & 3-30 \\\Leftrightarrow & \color{red}{-104} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-104} & & \\\Leftrightarrow & x = \frac{27}{104} & & \\ & V = \left\{ \frac{27}{104} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{9})& = & -8x+\frac{7}{4} \\\Leftrightarrow & -15x+\frac{20}{9}& = & -8x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-288}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{+80} & = & \color{red}{-288x} +63 \\\Leftrightarrow & -540x \color{red}{+80} \color{blue}{-80} \color{blue}{+288x} & = & \color{red}{-288x} +63 \color{blue}{+288x} \color{blue}{-80} \\\Leftrightarrow & -540x+288x& = & 63-80 \\\Leftrightarrow & \color{red}{-252} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-252} & & \\\Leftrightarrow & x = \frac{17}{252} & & \\ & V = \left\{ \frac{17}{252} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-30x} +21 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +21 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & -72x+30x& = & 21+16 \\\Leftrightarrow & \color{red}{-42} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-42} & & \\\Leftrightarrow & x = \frac{-37}{42} & & \\ & V = \left\{ \frac{-37}{42} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 990x+275x& = & 25-132 \\\Leftrightarrow & \color{red}{1265} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1265} & & \\ & V = \left\{ \frac{-107}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{-72} & = & \color{red}{308x} +77 \\\Leftrightarrow & -1320x \color{red}{-72} \color{blue}{+72} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{+72} \\\Leftrightarrow & -1320x-308x& = & 77+72 \\\Leftrightarrow & \color{red}{-1628} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1628} & & \\\Leftrightarrow & x = \frac{-149}{1628} & & \\ & V = \left\{ \frac{-149}{1628} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{15}{11}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-30} & = & \color{red}{-66x} +77 \\\Leftrightarrow & 220x \color{red}{-30} \color{blue}{+30} \color{blue}{+66x} & = & \color{red}{-66x} +77 \color{blue}{+66x} \color{blue}{+30} \\\Leftrightarrow & 220x+66x& = & 77+30 \\\Leftrightarrow & \color{red}{286} x& = & 107 \\\Leftrightarrow & x = \frac{107}{286} & & \\ & V = \left\{ \frac{107}{286} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-19 22:07:24
Een site van Busleyden Atheneum Mechelen