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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+56} & = & \color{red}{63x} +6 \\\Leftrightarrow & 210x \color{red}{+56} \color{blue}{-56} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-56} \\\Leftrightarrow & 210x-63x& = & 6-56 \\\Leftrightarrow & \color{red}{147} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{147} & & \\ & V = \left\{ \frac{-50}{147} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-189x} +30 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & 210x+189x& = & 30+56 \\\Leftrightarrow & \color{red}{399} x& = & 86 \\\Leftrightarrow & x = \frac{86}{399} & & \\ & V = \left\{ \frac{86}{399} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{7})& = & -3x+\frac{2}{7} \\\Leftrightarrow & -20x+\frac{12}{7}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+12} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -140x \color{red}{+12} \color{blue}{-12} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{-12} \\\Leftrightarrow & -140x+21x& = & 2-12 \\\Leftrightarrow & \color{red}{-119} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-119} & & \\\Leftrightarrow & x = \frac{10}{119} & & \\ & V = \left\{ \frac{10}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{20}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+20} & = & \color{red}{-9x} +10 \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{-20} \\\Leftrightarrow & 24x+9x& = & 10-20 \\\Leftrightarrow & \color{red}{33} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{33} & & \\ & V = \left\{ \frac{-10}{33} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -264x \color{red}{-36} \color{blue}{+36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{+36} \\\Leftrightarrow & -264x+110x& = & 33+36 \\\Leftrightarrow & \color{red}{-154} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-154} & & \\\Leftrightarrow & x = \frac{-69}{154} & & \\ & V = \left\{ \frac{-69}{154} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{6})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{35}{6}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{-175} & = & \color{red}{-270x} +36 \\\Leftrightarrow & 840x \color{red}{-175} \color{blue}{+175} \color{blue}{+270x} & = & \color{red}{-270x} +36 \color{blue}{+270x} \color{blue}{+175} \\\Leftrightarrow & 840x+270x& = & 36+175 \\\Leftrightarrow & \color{red}{1110} x& = & 211 \\\Leftrightarrow & x = \frac{211}{1110} & & \\ & V = \left\{ \frac{211}{1110} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{8}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-88} & = & \color{red}{-275x} +10 \\\Leftrightarrow & -660x \color{red}{-88} \color{blue}{+88} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+88} \\\Leftrightarrow & -660x+275x& = & 10+88 \\\Leftrightarrow & \color{red}{-385} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-385} & & \\\Leftrightarrow & x = \frac{-14}{55} & & \\ & V = \left\{ \frac{-14}{55} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{-66} & = & \color{red}{539x} +14 \\\Leftrightarrow & -693x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & -693x-539x& = & 14+66 \\\Leftrightarrow & \color{red}{-1232} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1232} & & \\\Leftrightarrow & x = \frac{-5}{77} & & \\ & V = \left\{ \frac{-5}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{-28x} +5 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{+28x} & = & \color{red}{-28x} +5 \color{blue}{+28x} \color{blue}{+15} \\\Leftrightarrow & -24x+28x& = & 5+15 \\\Leftrightarrow & \color{red}{4} x& = & 20 \\\Leftrightarrow & x = \frac{20}{4} & & \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & 4x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{20}{11}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{40}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+40} & = & \color{red}{88x} +99 \\\Leftrightarrow & 330x \color{red}{+40} \color{blue}{-40} \color{blue}{-88x} & = & \color{red}{88x} +99 \color{blue}{-88x} \color{blue}{-40} \\\Leftrightarrow & 330x-88x& = & 99-40 \\\Leftrightarrow & \color{red}{242} x& = & 59 \\\Leftrightarrow & x = \frac{59}{242} & & \\ & V = \left\{ \frac{59}{242} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{5})& = & -3x+\frac{9}{8} \\\Leftrightarrow & -14x-\frac{28}{5}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x- \frac{224}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{-224} & = & \color{red}{-120x} +45 \\\Leftrightarrow & -560x \color{red}{-224} \color{blue}{+224} \color{blue}{+120x} & = & \color{red}{-120x} +45 \color{blue}{+120x} \color{blue}{+224} \\\Leftrightarrow & -560x+120x& = & 45+224 \\\Leftrightarrow & \color{red}{-440} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-440} & & \\\Leftrightarrow & x = \frac{-269}{440} & & \\ & V = \left\{ \frac{-269}{440} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-56} & = & \color{red}{-147x} +24 \\\Leftrightarrow & -126x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +24 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & -126x+147x& = & 24+56 \\\Leftrightarrow & \color{red}{21} x& = & 80 \\\Leftrightarrow & x = \frac{80}{21} & & \\ & V = \left\{ \frac{80}{21} \right\} & \\\end{align}\)
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