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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{10})& = & -4x+\frac{3}{10} \\\Leftrightarrow & 35x+\frac{21}{10}& = & -4x+\frac{3}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+21} & = & \color{red}{-40x} +3 \\\Leftrightarrow & 350x \color{red}{+21} \color{blue}{-21} \color{blue}{+40x} & = & \color{red}{-40x} +3 \color{blue}{+40x} \color{blue}{-21} \\\Leftrightarrow & 350x+40x& = & 3-21 \\\Leftrightarrow & \color{red}{390} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{390} & & \\\Leftrightarrow & x = \frac{-3}{65} & & \\ & V = \left\{ \frac{-3}{65} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{8}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1120}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1120x \color{red}{-80} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -1120x \color{red}{-80} \color{blue}{+80} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{+80} \\\Leftrightarrow & -1120x+490x& = & 63+80 \\\Leftrightarrow & \color{red}{-630} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-630} & & \\\Leftrightarrow & x = \frac{-143}{630} & & \\ & V = \left\{ \frac{-143}{630} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{8}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-99x} +22 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{+24} \\\Leftrightarrow & -264x+99x& = & 22+24 \\\Leftrightarrow & \color{red}{-165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-165} & & \\\Leftrightarrow & x = \frac{-46}{165} & & \\ & V = \left\{ \frac{-46}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-110} & = & \color{red}{-308x} +70 \\\Leftrightarrow & -1155x \color{red}{-110} \color{blue}{+110} \color{blue}{+308x} & = & \color{red}{-308x} +70 \color{blue}{+308x} \color{blue}{+110} \\\Leftrightarrow & -1155x+308x& = & 70+110 \\\Leftrightarrow & \color{red}{-847} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-847} & & \\\Leftrightarrow & x = \frac{-180}{847} & & \\ & V = \left\{ \frac{-180}{847} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+2)& = & -4x+\frac{4}{3} \\\Leftrightarrow & -28x-14& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{42}{ \color{blue}{3} })& = & (\frac{-12}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-42} & = & \color{red}{-12x} +4 \\\Leftrightarrow & -84x \color{red}{-42} \color{blue}{+42} \color{blue}{+12x} & = & \color{red}{-12x} +4 \color{blue}{+12x} \color{blue}{+42} \\\Leftrightarrow & -84x+12x& = & 4+42 \\\Leftrightarrow & \color{red}{-72} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-72} & & \\\Leftrightarrow & x = \frac{-23}{36} & & \\ & V = \left\{ \frac{-23}{36} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{10}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-50} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 225x \color{red}{-50} \color{blue}{+50} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+50} \\\Leftrightarrow & 225x+105x& = & 18+50 \\\Leftrightarrow & \color{red}{330} x& = & 68 \\\Leftrightarrow & x = \frac{68}{330} & & \\\Leftrightarrow & x = \frac{34}{165} & & \\ & V = \left\{ \frac{34}{165} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{5})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 35x-\frac{28}{5}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x- \frac{56}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{-56} & = & \color{red}{-90x} +45 \\\Leftrightarrow & 350x \color{red}{-56} \color{blue}{+56} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+56} \\\Leftrightarrow & 350x+90x& = & 45+56 \\\Leftrightarrow & \color{red}{440} x& = & 101 \\\Leftrightarrow & x = \frac{101}{440} & & \\ & V = \left\{ \frac{101}{440} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{6})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{6}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+125} & = & \color{red}{210x} +36 \\\Leftrightarrow & 300x \color{red}{+125} \color{blue}{-125} \color{blue}{-210x} & = & \color{red}{210x} +36 \color{blue}{-210x} \color{blue}{-125} \\\Leftrightarrow & 300x-210x& = & 36-125 \\\Leftrightarrow & \color{red}{90} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{90} & & \\ & V = \left\{ \frac{-89}{90} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{9})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-315x} +45 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+315x} & = & \color{red}{-315x} +45 \color{blue}{+315x} \color{blue}{+56} \\\Leftrightarrow & -252x+315x& = & 45+56 \\\Leftrightarrow & \color{red}{63} x& = & 101 \\\Leftrightarrow & x = \frac{101}{63} & & \\ & V = \left\{ \frac{101}{63} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{+30} & = & \color{red}{88x} +10 \\\Leftrightarrow & -198x \color{red}{+30} \color{blue}{-30} \color{blue}{-88x} & = & \color{red}{88x} +10 \color{blue}{-88x} \color{blue}{-30} \\\Leftrightarrow & -198x-88x& = & 10-30 \\\Leftrightarrow & \color{red}{-286} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-286} & & \\\Leftrightarrow & x = \frac{10}{143} & & \\ & V = \left\{ \frac{10}{143} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{9})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 16x+\frac{20}{9}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1440}{ \color{blue}{90} }x+ \frac{200}{ \color{blue}{90} })& = & (\frac{-810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1440x \color{red}{+200} & = & \color{red}{-810x} +27 \\\Leftrightarrow & 1440x \color{red}{+200} \color{blue}{-200} \color{blue}{+810x} & = & \color{red}{-810x} +27 \color{blue}{+810x} \color{blue}{-200} \\\Leftrightarrow & 1440x+810x& = & 27-200 \\\Leftrightarrow & \color{red}{2250} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{2250} & & \\ & V = \left\{ \frac{-173}{2250} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{-100} & = & \color{red}{-175x} +14 \\\Leftrightarrow & -875x \color{red}{-100} \color{blue}{+100} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{+100} \\\Leftrightarrow & -875x+175x& = & 14+100 \\\Leftrightarrow & \color{red}{-700} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-700} & & \\\Leftrightarrow & x = \frac{-57}{350} & & \\ & V = \left\{ \frac{-57}{350} \right\} & \\\end{align}\)
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