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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{7})& = & 3x+\frac{3}{8} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{+128} & = & \color{red}{168x} +21 \\\Leftrightarrow & 448x \color{red}{+128} \color{blue}{-128} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{-128} \\\Leftrightarrow & 448x-168x& = & 21-128 \\\Leftrightarrow & \color{red}{280} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{280} & & \\ & V = \left\{ \frac{-107}{280} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-100} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & -350x+245x& = & 42+100 \\\Leftrightarrow & \color{red}{-105} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-105} & & \\\Leftrightarrow & x = \frac{-142}{105} & & \\ & V = \left\{ \frac{-142}{105} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-504}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -504x \color{red}{+48} & = & \color{red}{280x} +49 \\\Leftrightarrow & -504x \color{red}{+48} \color{blue}{-48} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{-48} \\\Leftrightarrow & -504x-280x& = & 49-48 \\\Leftrightarrow & \color{red}{-784} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-784} & & \\\Leftrightarrow & x = \frac{-1}{784} & & \\ & V = \left\{ \frac{-1}{784} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{11})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{20}{11}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{160}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-160} & = & \color{red}{-440x} +99 \\\Leftrightarrow & -1056x \color{red}{-160} \color{blue}{+160} \color{blue}{+440x} & = & \color{red}{-440x} +99 \color{blue}{+440x} \color{blue}{+160} \\\Leftrightarrow & -1056x+440x& = & 99+160 \\\Leftrightarrow & \color{red}{-616} x& = & 259 \\\Leftrightarrow & x = \frac{259}{-616} & & \\\Leftrightarrow & x = \frac{-37}{88} & & \\ & V = \left\{ \frac{-37}{88} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{-50x} +25 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 120x+50x& = & 25+24 \\\Leftrightarrow & \color{red}{170} x& = & 49 \\\Leftrightarrow & x = \frac{49}{170} & & \\ & V = \left\{ \frac{49}{170} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{-147} & = & \color{red}{504x} +80 \\\Leftrightarrow & 1568x \color{red}{-147} \color{blue}{+147} \color{blue}{-504x} & = & \color{red}{504x} +80 \color{blue}{-504x} \color{blue}{+147} \\\Leftrightarrow & 1568x-504x& = & 80+147 \\\Leftrightarrow & \color{red}{1064} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1064} & & \\ & V = \left\{ \frac{227}{1064} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & -2x+\frac{10}{11} \\\Leftrightarrow & -28x+\frac{35}{3}& = & -2x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+385} & = & \color{red}{-66x} +30 \\\Leftrightarrow & -924x \color{red}{+385} \color{blue}{-385} \color{blue}{+66x} & = & \color{red}{-66x} +30 \color{blue}{+66x} \color{blue}{-385} \\\Leftrightarrow & -924x+66x& = & 30-385 \\\Leftrightarrow & \color{red}{-858} x& = & -355 \\\Leftrightarrow & x = \frac{-355}{-858} & & \\\Leftrightarrow & x = \frac{355}{858} & & \\ & V = \left\{ \frac{355}{858} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{10}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+10} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 60x \color{red}{+10} \color{blue}{-10} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-10} \\\Leftrightarrow & 60x+27x& = & 8-10 \\\Leftrightarrow & \color{red}{87} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{87} & & \\ & V = \left\{ \frac{-2}{87} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{2})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{9}{2}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-12}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -12x \color{red}{+9} & = & \color{red}{-14x} +5 \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+14x} & = & \color{red}{-14x} +5 \color{blue}{+14x} \color{blue}{-9} \\\Leftrightarrow & -12x+14x& = & 5-9 \\\Leftrightarrow & \color{red}{2} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{2} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{11})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -16x-\frac{8}{11}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-40} & = & \color{red}{385x} +22 \\\Leftrightarrow & -880x \color{red}{-40} \color{blue}{+40} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+40} \\\Leftrightarrow & -880x-385x& = & 22+40 \\\Leftrightarrow & \color{red}{-1265} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-1265} & & \\\Leftrightarrow & x = \frac{-62}{1265} & & \\ & V = \left\{ \frac{-62}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{2})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -25x+\frac{25}{2}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+225} & = & \color{red}{-90x} +4 \\\Leftrightarrow & -450x \color{red}{+225} \color{blue}{-225} \color{blue}{+90x} & = & \color{red}{-90x} +4 \color{blue}{+90x} \color{blue}{-225} \\\Leftrightarrow & -450x+90x& = & 4-225 \\\Leftrightarrow & \color{red}{-360} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-360} & & \\\Leftrightarrow & x = \frac{221}{360} & & \\ & V = \left\{ \frac{221}{360} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{147x} +70 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+60} \\\Leftrightarrow & 420x-147x& = & 70+60 \\\Leftrightarrow & \color{red}{273} x& = & 130 \\\Leftrightarrow & x = \frac{130}{273} & & \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
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