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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{10})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-18} & = & \color{red}{-100x} +15 \\\Leftrightarrow & -180x \color{red}{-18} \color{blue}{+18} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{+18} \\\Leftrightarrow & -180x+100x& = & 15+18 \\\Leftrightarrow & \color{red}{-80} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-80} & & \\\Leftrightarrow & x = \frac{-33}{80} & & \\ & V = \left\{ \frac{-33}{80} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+154} & = & \color{red}{-264x} +18 \\\Leftrightarrow & -693x \color{red}{+154} \color{blue}{-154} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{-154} \\\Leftrightarrow & -693x+264x& = & 18-154 \\\Leftrightarrow & \color{red}{-429} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-429} & & \\\Leftrightarrow & x = \frac{136}{429} & & \\ & V = \left\{ \frac{136}{429} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{9}{11} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+132} & = & \color{red}{275x} +45 \\\Leftrightarrow & -1320x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +45 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -1320x-275x& = & 45-132 \\\Leftrightarrow & \color{red}{-1595} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-1595} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{6})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 28x+\frac{35}{6}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1176}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1176x \color{red}{+245} & = & \color{red}{126x} +60 \\\Leftrightarrow & 1176x \color{red}{+245} \color{blue}{-245} \color{blue}{-126x} & = & \color{red}{126x} +60 \color{blue}{-126x} \color{blue}{-245} \\\Leftrightarrow & 1176x-126x& = & 60-245 \\\Leftrightarrow & \color{red}{1050} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{1050} & & \\\Leftrightarrow & x = \frac{-37}{210} & & \\ & V = \left\{ \frac{-37}{210} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+220} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 770x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & 770x+231x& = & 42-220 \\\Leftrightarrow & \color{red}{1001} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{1001} & & \\ & V = \left\{ \frac{-178}{1001} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{11})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+180} & = & \color{red}{-550x} +77 \\\Leftrightarrow & -1320x \color{red}{+180} \color{blue}{-180} \color{blue}{+550x} & = & \color{red}{-550x} +77 \color{blue}{+550x} \color{blue}{-180} \\\Leftrightarrow & -1320x+550x& = & 77-180 \\\Leftrightarrow & \color{red}{-770} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-770} & & \\\Leftrightarrow & x = \frac{103}{770} & & \\ & V = \left\{ \frac{103}{770} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{+48} & = & \color{red}{440x} +77 \\\Leftrightarrow & -792x \color{red}{+48} \color{blue}{-48} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{-48} \\\Leftrightarrow & -792x-440x& = & 77-48 \\\Leftrightarrow & \color{red}{-1232} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-1232} & & \\\Leftrightarrow & x = \frac{-29}{1232} & & \\ & V = \left\{ \frac{-29}{1232} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-40} & = & \color{red}{196x} +63 \\\Leftrightarrow & -168x \color{red}{-40} \color{blue}{+40} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+40} \\\Leftrightarrow & -168x-196x& = & 63+40 \\\Leftrightarrow & \color{red}{-364} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-364} & & \\\Leftrightarrow & x = \frac{-103}{364} & & \\ & V = \left\{ \frac{-103}{364} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -25x-\frac{10}{3}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-375}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -375x \color{red}{-50} & = & \color{red}{135x} +12 \\\Leftrightarrow & -375x \color{red}{-50} \color{blue}{+50} \color{blue}{-135x} & = & \color{red}{135x} +12 \color{blue}{-135x} \color{blue}{+50} \\\Leftrightarrow & -375x-135x& = & 12+50 \\\Leftrightarrow & \color{red}{-510} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-510} & & \\\Leftrightarrow & x = \frac{-31}{255} & & \\ & V = \left\{ \frac{-31}{255} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{15}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-75} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 330x \color{red}{-75} \color{blue}{+75} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+75} \\\Leftrightarrow & 330x+275x& = & 66+75 \\\Leftrightarrow & \color{red}{605} x& = & 141 \\\Leftrightarrow & x = \frac{141}{605} & & \\ & V = \left\{ \frac{141}{605} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{120x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{-120x} & = & \color{red}{120x} +48 \color{blue}{-120x} \color{blue}{-105} \\\Leftrightarrow & -560x-120x& = & 48-105 \\\Leftrightarrow & \color{red}{-680} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-680} & & \\\Leftrightarrow & x = \frac{57}{680} & & \\ & V = \left\{ \frac{57}{680} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{11})& = & -9x+\frac{7}{11} \\\Leftrightarrow & 28x+\frac{35}{11}& = & -9x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{+35} & = & \color{red}{-99x} +7 \\\Leftrightarrow & 308x \color{red}{+35} \color{blue}{-35} \color{blue}{+99x} & = & \color{red}{-99x} +7 \color{blue}{+99x} \color{blue}{-35} \\\Leftrightarrow & 308x+99x& = & 7-35 \\\Leftrightarrow & \color{red}{407} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{407} & & \\ & V = \left\{ \frac{-28}{407} \right\} & \\\end{align}\)
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