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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1584}{ \color{blue}{66} }x- \frac{144}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1584x \color{red}{-144} & = & \color{red}{-462x} +77 \\\Leftrightarrow & -1584x \color{red}{-144} \color{blue}{+144} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{+144} \\\Leftrightarrow & -1584x+462x& = & 77+144 \\\Leftrightarrow & \color{red}{-1122} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1122} & & \\\Leftrightarrow & x = \frac{-13}{66} & & \\ & V = \left\{ \frac{-13}{66} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{5})& = & 8x+\frac{6}{7} \\\Leftrightarrow & -21x+\frac{28}{5}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-735}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -735x \color{red}{+196} & = & \color{red}{280x} +30 \\\Leftrightarrow & -735x \color{red}{+196} \color{blue}{-196} \color{blue}{-280x} & = & \color{red}{280x} +30 \color{blue}{-280x} \color{blue}{-196} \\\Leftrightarrow & -735x-280x& = & 30-196 \\\Leftrightarrow & \color{red}{-1015} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-1015} & & \\\Leftrightarrow & x = \frac{166}{1015} & & \\ & V = \left\{ \frac{166}{1015} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 6x+\frac{4}{5}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{+16} & = & \color{red}{-100x} +15 \\\Leftrightarrow & 120x \color{red}{+16} \color{blue}{-16} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{-16} \\\Leftrightarrow & 120x+100x& = & 15-16 \\\Leftrightarrow & \color{red}{220} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{220} & & \\ & V = \left\{ \frac{-1}{220} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{24}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+168} & = & \color{red}{175x} +15 \\\Leftrightarrow & 420x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & 420x-175x& = & 15-168 \\\Leftrightarrow & \color{red}{245} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{245} & & \\ & V = \left\{ \frac{-153}{245} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x+\frac{12}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+132} & = & \color{red}{539x} +21 \\\Leftrightarrow & -462x \color{red}{+132} \color{blue}{-132} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{-132} \\\Leftrightarrow & -462x-539x& = & 21-132 \\\Leftrightarrow & \color{red}{-1001} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{-1001} & & \\\Leftrightarrow & x = \frac{111}{1001} & & \\ & V = \left\{ \frac{111}{1001} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-147x} +56 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 126x+147x& = & 56+18 \\\Leftrightarrow & \color{red}{273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{273} & & \\ & V = \left\{ \frac{74}{273} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -4x-\frac{10}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-50} & = & \color{red}{135x} +6 \\\Leftrightarrow & -60x \color{red}{-50} \color{blue}{+50} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{+50} \\\Leftrightarrow & -60x-135x& = & 6+50 \\\Leftrightarrow & \color{red}{-195} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-195} & & \\\Leftrightarrow & x = \frac{-56}{195} & & \\ & V = \left\{ \frac{-56}{195} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & 9x+\frac{7}{9} \\\Leftrightarrow & -28x+\frac{21}{11}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x+ \frac{189}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{+189} & = & \color{red}{891x} +77 \\\Leftrightarrow & -2772x \color{red}{+189} \color{blue}{-189} \color{blue}{-891x} & = & \color{red}{891x} +77 \color{blue}{-891x} \color{blue}{-189} \\\Leftrightarrow & -2772x-891x& = & 77-189 \\\Leftrightarrow & \color{red}{-3663} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{-3663} & & \\\Leftrightarrow & x = \frac{112}{3663} & & \\ & V = \left\{ \frac{112}{3663} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-150} & = & \color{red}{-275x} +44 \\\Leftrightarrow & 990x \color{red}{-150} \color{blue}{+150} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{+150} \\\Leftrightarrow & 990x+275x& = & 44+150 \\\Leftrightarrow & \color{red}{1265} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1265} & & \\ & V = \left\{ \frac{194}{1265} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-504}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -504x \color{red}{-180} & = & \color{red}{210x} +35 \\\Leftrightarrow & -504x \color{red}{-180} \color{blue}{+180} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+180} \\\Leftrightarrow & -504x-210x& = & 35+180 \\\Leftrightarrow & \color{red}{-714} x& = & 215 \\\Leftrightarrow & x = \frac{215}{-714} & & \\\Leftrightarrow & x = \frac{-215}{714} & & \\ & V = \left\{ \frac{-215}{714} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 24x-\frac{30}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-270} & = & \color{red}{-495x} +44 \\\Leftrightarrow & 2376x \color{red}{-270} \color{blue}{+270} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{+270} \\\Leftrightarrow & 2376x+495x& = & 44+270 \\\Leftrightarrow & \color{red}{2871} x& = & 314 \\\Leftrightarrow & x = \frac{314}{2871} & & \\ & V = \left\{ \frac{314}{2871} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{11})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -25x-\frac{25}{11}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2750}{ \color{blue}{110} }x- \frac{250}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2750x \color{red}{-250} & = & \color{red}{330x} +99 \\\Leftrightarrow & -2750x \color{red}{-250} \color{blue}{+250} \color{blue}{-330x} & = & \color{red}{330x} +99 \color{blue}{-330x} \color{blue}{+250} \\\Leftrightarrow & -2750x-330x& = & 99+250 \\\Leftrightarrow & \color{red}{-3080} x& = & 349 \\\Leftrightarrow & x = \frac{349}{-3080} & & \\\Leftrightarrow & x = \frac{-349}{3080} & & \\ & V = \left\{ \frac{-349}{3080} \right\} & \\\end{align}\)
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