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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-88} & = & \color{red}{-99x} +18 \\\Leftrightarrow & -264x \color{red}{-88} \color{blue}{+88} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{+88} \\\Leftrightarrow & -264x+99x& = & 18+88 \\\Leftrightarrow & \color{red}{-165} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-165} & & \\\Leftrightarrow & x = \frac{-106}{165} & & \\ & V = \left\{ \frac{-106}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+12} & = & \color{red}{25x} +8 \\\Leftrightarrow & -45x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -45x-25x& = & 8-12 \\\Leftrightarrow & \color{red}{-70} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-70} & & \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{72x} +7 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +7 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & 224x-72x& = & 7+21 \\\Leftrightarrow & \color{red}{152} x& = & 28 \\\Leftrightarrow & x = \frac{28}{152} & & \\\Leftrightarrow & x = \frac{7}{38} & & \\ & V = \left\{ \frac{7}{38} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-90} & = & \color{red}{105x} +70 \\\Leftrightarrow & -252x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & -252x-105x& = & 70+90 \\\Leftrightarrow & \color{red}{-357} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-357} & & \\\Leftrightarrow & x = \frac{-160}{357} & & \\ & V = \left\{ \frac{-160}{357} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & 8x+\frac{5}{7} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 8x+\frac{5}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{10}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-105} & = & \color{red}{112x} +10 \\\Leftrightarrow & -210x \color{red}{-105} \color{blue}{+105} \color{blue}{-112x} & = & \color{red}{112x} +10 \color{blue}{-112x} \color{blue}{+105} \\\Leftrightarrow & -210x-112x& = & 10+105 \\\Leftrightarrow & \color{red}{-322} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-322} & & \\\Leftrightarrow & x = \frac{-5}{14} & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{6}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-396}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -396x \color{red}{-24} & = & \color{red}{-220x} +99 \\\Leftrightarrow & -396x \color{red}{-24} \color{blue}{+24} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+24} \\\Leftrightarrow & -396x+220x& = & 99+24 \\\Leftrightarrow & \color{red}{-176} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-176} & & \\\Leftrightarrow & x = \frac{-123}{176} & & \\ & V = \left\{ \frac{-123}{176} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x- \frac{50}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{-50} & = & \color{red}{28x} +3 \\\Leftrightarrow & -80x \color{red}{-50} \color{blue}{+50} \color{blue}{-28x} & = & \color{red}{28x} +3 \color{blue}{-28x} \color{blue}{+50} \\\Leftrightarrow & -80x-28x& = & 3+50 \\\Leftrightarrow & \color{red}{-108} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-108} & & \\\Leftrightarrow & x = \frac{-53}{108} & & \\ & V = \left\{ \frac{-53}{108} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & 168x+105x& = & 18+56 \\\Leftrightarrow & \color{red}{273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{273} & & \\ & V = \left\{ \frac{74}{273} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{-36} & = & \color{red}{-110x} +55 \\\Leftrightarrow & 528x \color{red}{-36} \color{blue}{+36} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{+36} \\\Leftrightarrow & 528x+110x& = & 55+36 \\\Leftrightarrow & \color{red}{638} x& = & 91 \\\Leftrightarrow & x = \frac{91}{638} & & \\ & V = \left\{ \frac{91}{638} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x+ \frac{32}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{+32} & = & \color{red}{66x} +55 \\\Leftrightarrow & 352x \color{red}{+32} \color{blue}{-32} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{-32} \\\Leftrightarrow & 352x-66x& = & 55-32 \\\Leftrightarrow & \color{red}{286} x& = & 23 \\\Leftrightarrow & x = \frac{23}{286} & & \\ & V = \left\{ \frac{23}{286} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+30} & = & \color{red}{63x} +5 \\\Leftrightarrow & -54x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & -54x-63x& = & 5-30 \\\Leftrightarrow & \color{red}{-117} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-117} & & \\\Leftrightarrow & x = \frac{25}{117} & & \\ & V = \left\{ \frac{25}{117} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-216} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 540x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 540x+225x& = & 40+216 \\\Leftrightarrow & \color{red}{765} x& = & 256 \\\Leftrightarrow & x = \frac{256}{765} & & \\ & V = \left\{ \frac{256}{765} \right\} & \\\end{align}\)
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