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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{25x} +4 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & 90x-25x& = & 4-24 \\\Leftrightarrow & \color{red}{65} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{65} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{9})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 8x-\frac{4}{9}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{720}{ \color{blue}{90} }x- \frac{40}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 720x \color{red}{-40} & = & \color{red}{-630x} +63 \\\Leftrightarrow & 720x \color{red}{-40} \color{blue}{+40} \color{blue}{+630x} & = & \color{red}{-630x} +63 \color{blue}{+630x} \color{blue}{+40} \\\Leftrightarrow & 720x+630x& = & 63+40 \\\Leftrightarrow & \color{red}{1350} x& = & 103 \\\Leftrightarrow & x = \frac{103}{1350} & & \\ & V = \left\{ \frac{103}{1350} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+15} & = & \color{red}{-56x} +36 \\\Leftrightarrow & -160x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -160x+56x& = & 36-15 \\\Leftrightarrow & \color{red}{-104} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-104} & & \\\Leftrightarrow & x = \frac{-21}{104} & & \\ & V = \left\{ \frac{-21}{104} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+84} & = & \color{red}{245x} +25 \\\Leftrightarrow & 525x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & 525x-245x& = & 25-84 \\\Leftrightarrow & \color{red}{280} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{280} & & \\ & V = \left\{ \frac{-59}{280} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+66} & = & \color{red}{-539x} +49 \\\Leftrightarrow & -770x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +49 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -770x+539x& = & 49-66 \\\Leftrightarrow & \color{red}{-231} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-231} & & \\\Leftrightarrow & x = \frac{17}{231} & & \\ & V = \left\{ \frac{17}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+98} & = & \color{red}{-189x} +9 \\\Leftrightarrow & 588x \color{red}{+98} \color{blue}{-98} \color{blue}{+189x} & = & \color{red}{-189x} +9 \color{blue}{+189x} \color{blue}{-98} \\\Leftrightarrow & 588x+189x& = & 9-98 \\\Leftrightarrow & \color{red}{777} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{777} & & \\ & V = \left\{ \frac{-89}{777} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{3})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{27x} +2 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+8} \\\Leftrightarrow & -24x-27x& = & 2+8 \\\Leftrightarrow & \color{red}{-51} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-51} & & \\\Leftrightarrow & x = \frac{-10}{51} & & \\ & V = \left\{ \frac{-10}{51} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{77x} +4 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-18} \\\Leftrightarrow & -330x-77x& = & 4-18 \\\Leftrightarrow & \color{red}{-407} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-407} & & \\\Leftrightarrow & x = \frac{14}{407} & & \\ & V = \left\{ \frac{14}{407} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{5})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 28x+\frac{28}{5}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{980}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 980x \color{red}{+196} & = & \color{red}{-315x} +20 \\\Leftrightarrow & 980x \color{red}{+196} \color{blue}{-196} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-196} \\\Leftrightarrow & 980x+315x& = & 20-196 \\\Leftrightarrow & \color{red}{1295} x& = & -176 \\\Leftrightarrow & x = \frac{-176}{1295} & & \\ & V = \left\{ \frac{-176}{1295} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 2x+\frac{5}{6} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{48x} +20 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{-48x} & = & \color{red}{48x} +20 \color{blue}{-48x} \color{blue}{-63} \\\Leftrightarrow & -672x-48x& = & 20-63 \\\Leftrightarrow & \color{red}{-720} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-720} & & \\\Leftrightarrow & x = \frac{43}{720} & & \\ & V = \left\{ \frac{43}{720} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{11})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{21}{11}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-63} & = & \color{red}{297x} +22 \\\Leftrightarrow & 924x \color{red}{-63} \color{blue}{+63} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{+63} \\\Leftrightarrow & 924x-297x& = & 22+63 \\\Leftrightarrow & \color{red}{627} x& = & 85 \\\Leftrightarrow & x = \frac{85}{627} & & \\ & V = \left\{ \frac{85}{627} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{10}{11}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-10} & = & \color{red}{-44x} +2 \\\Leftrightarrow & -165x \color{red}{-10} \color{blue}{+10} \color{blue}{+44x} & = & \color{red}{-44x} +2 \color{blue}{+44x} \color{blue}{+10} \\\Leftrightarrow & -165x+44x& = & 2+10 \\\Leftrightarrow & \color{red}{-121} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-121} & & \\\Leftrightarrow & x = \frac{-12}{121} & & \\ & V = \left\{ \frac{-12}{121} \right\} & \\\end{align}\)
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