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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{16}{11}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x+ \frac{128}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{+128} & = & \color{red}{-440x} +33 \\\Leftrightarrow & 1056x \color{red}{+128} \color{blue}{-128} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{-128} \\\Leftrightarrow & 1056x+440x& = & 33-128 \\\Leftrightarrow & \color{red}{1496} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{1496} & & \\ & V = \left\{ \frac{-95}{1496} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{10}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{-99x} +22 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{+30} \\\Leftrightarrow & 660x+99x& = & 22+30 \\\Leftrightarrow & \color{red}{759} x& = & 52 \\\Leftrightarrow & x = \frac{52}{759} & & \\ & V = \left\{ \frac{52}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{30}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-210} & = & \color{red}{539x} +110 \\\Leftrightarrow & 924x \color{red}{-210} \color{blue}{+210} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+210} \\\Leftrightarrow & 924x-539x& = & 110+210 \\\Leftrightarrow & \color{red}{385} x& = & 320 \\\Leftrightarrow & x = \frac{320}{385} & & \\\Leftrightarrow & x = \frac{64}{77} & & \\ & V = \left\{ \frac{64}{77} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{+10} & = & \color{red}{77x} +4 \\\Leftrightarrow & 44x \color{red}{+10} \color{blue}{-10} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-10} \\\Leftrightarrow & 44x-77x& = & 4-10 \\\Leftrightarrow & \color{red}{-33} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-33} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{4}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+28} & = & \color{red}{-385x} +110 \\\Leftrightarrow & -308x \color{red}{+28} \color{blue}{-28} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-28} \\\Leftrightarrow & -308x+385x& = & 110-28 \\\Leftrightarrow & \color{red}{77} x& = & 82 \\\Leftrightarrow & x = \frac{82}{77} & & \\ & V = \left\{ \frac{82}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-176} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 924x \color{red}{-176} \color{blue}{+176} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+176} \\\Leftrightarrow & 924x+385x& = & 14+176 \\\Leftrightarrow & \color{red}{1309} x& = & 190 \\\Leftrightarrow & x = \frac{190}{1309} & & \\ & V = \left\{ \frac{190}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{4})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+165} & = & \color{red}{-220x} +24 \\\Leftrightarrow & -528x \color{red}{+165} \color{blue}{-165} \color{blue}{+220x} & = & \color{red}{-220x} +24 \color{blue}{+220x} \color{blue}{-165} \\\Leftrightarrow & -528x+220x& = & 24-165 \\\Leftrightarrow & \color{red}{-308} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-308} & & \\\Leftrightarrow & x = \frac{141}{308} & & \\ & V = \left\{ \frac{141}{308} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 6x+\frac{8}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+64} & = & \color{red}{280x} +35 \\\Leftrightarrow & 240x \color{red}{+64} \color{blue}{-64} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{-64} \\\Leftrightarrow & 240x-280x& = & 35-64 \\\Leftrightarrow & \color{red}{-40} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-40} & & \\\Leftrightarrow & x = \frac{29}{40} & & \\ & V = \left\{ \frac{29}{40} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{-616x} +32 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{+616x} & = & \color{red}{-616x} +32 \color{blue}{+616x} \color{blue}{-165} \\\Leftrightarrow & 1320x+616x& = & 32-165 \\\Leftrightarrow & \color{red}{1936} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{1936} & & \\ & V = \left\{ \frac{-133}{1936} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-18} \\\Leftrightarrow & -126x+147x& = & 28-18 \\\Leftrightarrow & \color{red}{21} x& = & 10 \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{5})& = & 6x+\frac{2}{11} \\\Leftrightarrow & -35x-\frac{14}{5}& = & 6x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-154} & = & \color{red}{330x} +10 \\\Leftrightarrow & -1925x \color{red}{-154} \color{blue}{+154} \color{blue}{-330x} & = & \color{red}{330x} +10 \color{blue}{-330x} \color{blue}{+154} \\\Leftrightarrow & -1925x-330x& = & 10+154 \\\Leftrightarrow & \color{red}{-2255} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-2255} & & \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{6}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+18} & = & \color{red}{105x} +40 \\\Leftrightarrow & -150x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & -150x-105x& = & 40-18 \\\Leftrightarrow & \color{red}{-255} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-255} & & \\\Leftrightarrow & x = \frac{-22}{255} & & \\ & V = \left\{ \frac{-22}{255} \right\} & \\\end{align}\)
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