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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -8x+\frac{5}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-264x} +15 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+264x} & = & \color{red}{-264x} +15 \color{blue}{+264x} \color{blue}{+154} \\\Leftrightarrow & 1155x+264x& = & 15+154 \\\Leftrightarrow & \color{red}{1419} x& = & 169 \\\Leftrightarrow & x = \frac{169}{1419} & & \\ & V = \left\{ \frac{169}{1419} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 20x-\frac{20}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{20}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-20} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 220x \color{red}{-20} \color{blue}{+20} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{+20} \\\Leftrightarrow & 220x+77x& = & 2+20 \\\Leftrightarrow & \color{red}{297} x& = & 22 \\\Leftrightarrow & x = \frac{22}{297} & & \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-66} & = & \color{red}{385x} +25 \\\Leftrightarrow & -550x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -550x-385x& = & 25+66 \\\Leftrightarrow & \color{red}{-935} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-935} & & \\\Leftrightarrow & x = \frac{-91}{935} & & \\ & V = \left\{ \frac{-91}{935} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{7})& = & 4x+\frac{5}{9} \\\Leftrightarrow & -15x+\frac{15}{7}& = & 4x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+135} & = & \color{red}{252x} +35 \\\Leftrightarrow & -945x \color{red}{+135} \color{blue}{-135} \color{blue}{-252x} & = & \color{red}{252x} +35 \color{blue}{-252x} \color{blue}{-135} \\\Leftrightarrow & -945x-252x& = & 35-135 \\\Leftrightarrow & \color{red}{-1197} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-1197} & & \\\Leftrightarrow & x = \frac{100}{1197} & & \\ & V = \left\{ \frac{100}{1197} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{231x} +44 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-60} \\\Leftrightarrow & 660x-231x& = & 44-60 \\\Leftrightarrow & \color{red}{429} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{429} & & \\ & V = \left\{ \frac{-16}{429} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{10})& = & -6x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{21}{10}& = & -6x+\frac{10}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2450}{ \color{blue}{70} }x- \frac{147}{ \color{blue}{70} })& = & (\frac{-420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2450x \color{red}{-147} & = & \color{red}{-420x} +100 \\\Leftrightarrow & -2450x \color{red}{-147} \color{blue}{+147} \color{blue}{+420x} & = & \color{red}{-420x} +100 \color{blue}{+420x} \color{blue}{+147} \\\Leftrightarrow & -2450x+420x& = & 100+147 \\\Leftrightarrow & \color{red}{-2030} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-2030} & & \\\Leftrightarrow & x = \frac{-247}{2030} & & \\ & V = \left\{ \frac{-247}{2030} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{7})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{4}{7}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{36}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-36} & = & \color{red}{-567x} +28 \\\Leftrightarrow & -504x \color{red}{-36} \color{blue}{+36} \color{blue}{+567x} & = & \color{red}{-567x} +28 \color{blue}{+567x} \color{blue}{+36} \\\Leftrightarrow & -504x+567x& = & 28+36 \\\Leftrightarrow & \color{red}{63} x& = & 64 \\\Leftrightarrow & x = \frac{64}{63} & & \\ & V = \left\{ \frac{64}{63} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{6})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -25x-\frac{25}{6}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-25} & = & \color{red}{24x} +8 \\\Leftrightarrow & -150x \color{red}{-25} \color{blue}{+25} \color{blue}{-24x} & = & \color{red}{24x} +8 \color{blue}{-24x} \color{blue}{+25} \\\Leftrightarrow & -150x-24x& = & 8+25 \\\Leftrightarrow & \color{red}{-174} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-174} & & \\\Leftrightarrow & x = \frac{-11}{58} & & \\ & V = \left\{ \frac{-11}{58} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{+12} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 132x \color{red}{+12} \color{blue}{-12} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{-12} \\\Leftrightarrow & 132x+110x& = & 99-12 \\\Leftrightarrow & \color{red}{242} x& = & 87 \\\Leftrightarrow & x = \frac{87}{242} & & \\ & V = \left\{ \frac{87}{242} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & -3x+\frac{3}{11} \\\Leftrightarrow & 16x+\frac{16}{3}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+176} & = & \color{red}{-99x} +9 \\\Leftrightarrow & 528x \color{red}{+176} \color{blue}{-176} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{-176} \\\Leftrightarrow & 528x+99x& = & 9-176 \\\Leftrightarrow & \color{red}{627} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{627} & & \\ & V = \left\{ \frac{-167}{627} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +88 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 88-54 \\\Leftrightarrow & \color{red}{-1221} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-1221} & & \\\Leftrightarrow & x = \frac{-34}{1221} & & \\ & V = \left\{ \frac{-34}{1221} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+2)& = & 2x+\frac{10}{7} \\\Leftrightarrow & 21x-14& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{147}{ \color{blue}{7} }x- \frac{98}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 147x \color{red}{-98} & = & \color{red}{14x} +10 \\\Leftrightarrow & 147x \color{red}{-98} \color{blue}{+98} \color{blue}{-14x} & = & \color{red}{14x} +10 \color{blue}{-14x} \color{blue}{+98} \\\Leftrightarrow & 147x-14x& = & 10+98 \\\Leftrightarrow & \color{red}{133} x& = & 108 \\\Leftrightarrow & x = \frac{108}{133} & & \\ & V = \left\{ \frac{108}{133} \right\} & \\\end{align}\)
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