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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{-72} & = & \color{red}{-210x} +25 \\\Leftrightarrow & -480x \color{red}{-72} \color{blue}{+72} \color{blue}{+210x} & = & \color{red}{-210x} +25 \color{blue}{+210x} \color{blue}{+72} \\\Leftrightarrow & -480x+210x& = & 25+72 \\\Leftrightarrow & \color{red}{-270} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-270} & & \\\Leftrightarrow & x = \frac{-97}{270} & & \\ & V = \left\{ \frac{-97}{270} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+70} & = & \color{red}{-120x} +18 \\\Leftrightarrow & -315x \color{red}{+70} \color{blue}{-70} \color{blue}{+120x} & = & \color{red}{-120x} +18 \color{blue}{+120x} \color{blue}{-70} \\\Leftrightarrow & -315x+120x& = & 18-70 \\\Leftrightarrow & \color{red}{-195} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-195} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -30x-\frac{24}{5}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{-96} & = & \color{red}{-140x} +35 \\\Leftrightarrow & -600x \color{red}{-96} \color{blue}{+96} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{+96} \\\Leftrightarrow & -600x+140x& = & 35+96 \\\Leftrightarrow & \color{red}{-460} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-460} & & \\\Leftrightarrow & x = \frac{-131}{460} & & \\ & V = \left\{ \frac{-131}{460} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{11})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-880}{ \color{blue}{110} }x- \frac{160}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -880x \color{red}{-160} & = & \color{red}{-990x} +33 \\\Leftrightarrow & -880x \color{red}{-160} \color{blue}{+160} \color{blue}{+990x} & = & \color{red}{-990x} +33 \color{blue}{+990x} \color{blue}{+160} \\\Leftrightarrow & -880x+990x& = & 33+160 \\\Leftrightarrow & \color{red}{110} x& = & 193 \\\Leftrightarrow & x = \frac{193}{110} & & \\ & V = \left\{ \frac{193}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{12}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-84} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1232x \color{red}{-84} \color{blue}{+84} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+84} \\\Leftrightarrow & 1232x+693x& = & 110+84 \\\Leftrightarrow & \color{red}{1925} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1925} & & \\ & V = \left\{ \frac{194}{1925} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{11})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-70} & = & \color{red}{-539x} +22 \\\Leftrightarrow & 1155x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +22 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & 1155x+539x& = & 22+70 \\\Leftrightarrow & \color{red}{1694} x& = & 92 \\\Leftrightarrow & x = \frac{92}{1694} & & \\\Leftrightarrow & x = \frac{46}{847} & & \\ & V = \left\{ \frac{46}{847} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & 9x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-105} & = & \color{red}{252x} +16 \\\Leftrightarrow & 280x \color{red}{-105} \color{blue}{+105} \color{blue}{-252x} & = & \color{red}{252x} +16 \color{blue}{-252x} \color{blue}{+105} \\\Leftrightarrow & 280x-252x& = & 16+105 \\\Leftrightarrow & \color{red}{28} x& = & 121 \\\Leftrightarrow & x = \frac{121}{28} & & \\ & V = \left\{ \frac{121}{28} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{16}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+48} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{+48} \color{blue}{-48} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-48} \\\Leftrightarrow & -396x-165x& = & 88-48 \\\Leftrightarrow & \color{red}{-561} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-561} & & \\\Leftrightarrow & x = \frac{-40}{561} & & \\ & V = \left\{ \frac{-40}{561} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{7})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 16x+\frac{8}{7}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{448}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 448x \color{red}{+32} & = & \color{red}{140x} +35 \\\Leftrightarrow & 448x \color{red}{+32} \color{blue}{-32} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{-32} \\\Leftrightarrow & 448x-140x& = & 35-32 \\\Leftrightarrow & \color{red}{308} x& = & 3 \\\Leftrightarrow & x = \frac{3}{308} & & \\ & V = \left\{ \frac{3}{308} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{-25x} +7 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+25x} & = & \color{red}{-25x} +7 \color{blue}{+25x} \color{blue}{-6} \\\Leftrightarrow & 30x+25x& = & 7-6 \\\Leftrightarrow & \color{red}{55} x& = & 1 \\\Leftrightarrow & x = \frac{1}{55} & & \\ & V = \left\{ \frac{1}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+56} & = & \color{red}{-147x} +30 \\\Leftrightarrow & 210x \color{red}{+56} \color{blue}{-56} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{-56} \\\Leftrightarrow & 210x+147x& = & 30-56 \\\Leftrightarrow & \color{red}{357} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{357} & & \\ & V = \left\{ \frac{-26}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+150} & = & \color{red}{140x} +14 \\\Leftrightarrow & -630x \color{red}{+150} \color{blue}{-150} \color{blue}{-140x} & = & \color{red}{140x} +14 \color{blue}{-140x} \color{blue}{-150} \\\Leftrightarrow & -630x-140x& = & 14-150 \\\Leftrightarrow & \color{red}{-770} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-770} & & \\\Leftrightarrow & x = \frac{68}{385} & & \\ & V = \left\{ \frac{68}{385} \right\} & \\\end{align}\)
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