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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-20} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+20} \\\Leftrightarrow & 30x+27x& = & 8+20 \\\Leftrightarrow & \color{red}{57} x& = & 28 \\\Leftrightarrow & x = \frac{28}{57} & & \\ & V = \left\{ \frac{28}{57} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+1)& = & -8x+\frac{5}{11} \\\Leftrightarrow & -28x-7& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x- \frac{77}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{-77} & = & \color{red}{-88x} +5 \\\Leftrightarrow & -308x \color{red}{-77} \color{blue}{+77} \color{blue}{+88x} & = & \color{red}{-88x} +5 \color{blue}{+88x} \color{blue}{+77} \\\Leftrightarrow & -308x+88x& = & 5+77 \\\Leftrightarrow & \color{red}{-220} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-220} & & \\\Leftrightarrow & x = \frac{-41}{110} & & \\ & V = \left\{ \frac{-41}{110} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{3})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 14x-\frac{35}{3}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-385} & = & \color{red}{99x} +6 \\\Leftrightarrow & 462x \color{red}{-385} \color{blue}{+385} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{+385} \\\Leftrightarrow & 462x-99x& = & 6+385 \\\Leftrightarrow & \color{red}{363} x& = & 391 \\\Leftrightarrow & x = \frac{391}{363} & & \\ & V = \left\{ \frac{391}{363} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{8})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{+189} & = & \color{red}{-216x} +16 \\\Leftrightarrow & 1008x \color{red}{+189} \color{blue}{-189} \color{blue}{+216x} & = & \color{red}{-216x} +16 \color{blue}{+216x} \color{blue}{-189} \\\Leftrightarrow & 1008x+216x& = & 16-189 \\\Leftrightarrow & \color{red}{1224} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{1224} & & \\ & V = \left\{ \frac{-173}{1224} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{8})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{25}{8}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{75}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-75} & = & \color{red}{96x} +32 \\\Leftrightarrow & -360x \color{red}{-75} \color{blue}{+75} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{+75} \\\Leftrightarrow & -360x-96x& = & 32+75 \\\Leftrightarrow & \color{red}{-456} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-456} & & \\\Leftrightarrow & x = \frac{-107}{456} & & \\ & V = \left\{ \frac{-107}{456} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{11})& = & 6x+\frac{7}{5} \\\Leftrightarrow & 35x+\frac{21}{11}& = & 6x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x+ \frac{105}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{+105} & = & \color{red}{330x} +77 \\\Leftrightarrow & 1925x \color{red}{+105} \color{blue}{-105} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{-105} \\\Leftrightarrow & 1925x-330x& = & 77-105 \\\Leftrightarrow & \color{red}{1595} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{1595} & & \\ & V = \left\{ \frac{-28}{1595} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -252x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & -252x+105x& = & 14+18 \\\Leftrightarrow & \color{red}{-147} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-147} & & \\\Leftrightarrow & x = \frac{-32}{147} & & \\ & V = \left\{ \frac{-32}{147} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+8} & = & \color{red}{-81x} +4 \\\Leftrightarrow & 90x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & 90x+81x& = & 4-8 \\\Leftrightarrow & \color{red}{171} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{171} & & \\ & V = \left\{ \frac{-4}{171} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-168} & = & \color{red}{245x} +45 \\\Leftrightarrow & -1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & -1050x-245x& = & 45+168 \\\Leftrightarrow & \color{red}{-1295} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-1295} & & \\\Leftrightarrow & x = \frac{-213}{1295} & & \\ & V = \left\{ \frac{-213}{1295} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-126} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 2310x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & 2310x+539x& = & 66+126 \\\Leftrightarrow & \color{red}{2849} x& = & 192 \\\Leftrightarrow & x = \frac{192}{2849} & & \\ & V = \left\{ \frac{192}{2849} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{5})& = & 9x+\frac{2}{11} \\\Leftrightarrow & 28x-\frac{14}{5}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-154} & = & \color{red}{495x} +10 \\\Leftrightarrow & 1540x \color{red}{-154} \color{blue}{+154} \color{blue}{-495x} & = & \color{red}{495x} +10 \color{blue}{-495x} \color{blue}{+154} \\\Leftrightarrow & 1540x-495x& = & 10+154 \\\Leftrightarrow & \color{red}{1045} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1045} & & \\ & V = \left\{ \frac{164}{1045} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{8}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+24} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -336x \color{red}{+24} \color{blue}{-24} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-24} \\\Leftrightarrow & -336x+147x& = & 14-24 \\\Leftrightarrow & \color{red}{-189} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-189} & & \\\Leftrightarrow & x = \frac{10}{189} & & \\ & V = \left\{ \frac{10}{189} \right\} & \\\end{align}\)
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