Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & 8x+\frac{2}{7} \\\Leftrightarrow & -25x-\frac{10}{7}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-10} & = & \color{red}{56x} +2 \\\Leftrightarrow & -175x \color{red}{-10} \color{blue}{+10} \color{blue}{-56x} & = & \color{red}{56x} +2 \color{blue}{-56x} \color{blue}{+10} \\\Leftrightarrow & -175x-56x& = & 2+10 \\\Leftrightarrow & \color{red}{-231} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-231} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -18x-\frac{24}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1008}{ \color{blue}{56} }x- \frac{192}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1008x \color{red}{-192} & = & \color{red}{280x} +49 \\\Leftrightarrow & -1008x \color{red}{-192} \color{blue}{+192} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{+192} \\\Leftrightarrow & -1008x-280x& = & 49+192 \\\Leftrightarrow & \color{red}{-1288} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-1288} & & \\\Leftrightarrow & x = \frac{-241}{1288} & & \\ & V = \left\{ \frac{-241}{1288} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 126x+105x& = & 35-18 \\\Leftrightarrow & \color{red}{231} x& = & 17 \\\Leftrightarrow & x = \frac{17}{231} & & \\ & V = \left\{ \frac{17}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-88} & = & \color{red}{-297x} +15 \\\Leftrightarrow & 132x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & 132x+297x& = & 15+88 \\\Leftrightarrow & \color{red}{429} x& = & 103 \\\Leftrightarrow & x = \frac{103}{429} & & \\ & V = \left\{ \frac{103}{429} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -270x+135x& = & 10+36 \\\Leftrightarrow & \color{red}{-135} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-135} & & \\\Leftrightarrow & x = \frac{-46}{135} & & \\ & V = \left\{ \frac{-46}{135} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{2})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{15}{2}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-165} & = & \color{red}{154x} +12 \\\Leftrightarrow & -220x \color{red}{-165} \color{blue}{+165} \color{blue}{-154x} & = & \color{red}{154x} +12 \color{blue}{-154x} \color{blue}{+165} \\\Leftrightarrow & -220x-154x& = & 12+165 \\\Leftrightarrow & \color{red}{-374} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-374} & & \\\Leftrightarrow & x = \frac{-177}{374} & & \\ & V = \left\{ \frac{-177}{374} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 28+18 \\\Leftrightarrow & \color{red}{-273} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-273} & & \\\Leftrightarrow & x = \frac{-46}{273} & & \\ & V = \left\{ \frac{-46}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 252x-105x& = & 56+18 \\\Leftrightarrow & \color{red}{147} x& = & 74 \\\Leftrightarrow & x = \frac{74}{147} & & \\ & V = \left\{ \frac{74}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-231x} +14 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +14 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & 770x+231x& = & 14-110 \\\Leftrightarrow & \color{red}{1001} x& = & -96 \\\Leftrightarrow & x = \frac{-96}{1001} & & \\ & V = \left\{ \frac{-96}{1001} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{-168} \\\Leftrightarrow & -840x+175x& = & 50-168 \\\Leftrightarrow & \color{red}{-665} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-665} & & \\\Leftrightarrow & x = \frac{118}{665} & & \\ & V = \left\{ \frac{118}{665} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & 4x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{28}{3}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-28} & = & \color{red}{12x} +2 \\\Leftrightarrow & 105x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +2 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & 105x-12x& = & 2+28 \\\Leftrightarrow & \color{red}{93} x& = & 30 \\\Leftrightarrow & x = \frac{30}{93} & & \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{7})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{126x} +21 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{+40} \\\Leftrightarrow & -280x-126x& = & 21+40 \\\Leftrightarrow & \color{red}{-406} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-406} & & \\\Leftrightarrow & x = \frac{-61}{406} & & \\ & V = \left\{ \frac{-61}{406} \right\} & \\\end{align}\)
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