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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{+147} & = & \color{red}{-280x} +80 \\\Leftrightarrow & 1176x \color{red}{+147} \color{blue}{-147} \color{blue}{+280x} & = & \color{red}{-280x} +80 \color{blue}{+280x} \color{blue}{-147} \\\Leftrightarrow & 1176x+280x& = & 80-147 \\\Leftrightarrow & \color{red}{1456} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{1456} & & \\ & V = \left\{ \frac{-67}{1456} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{7})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{4}{7}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+8} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 140x \color{red}{+8} \color{blue}{-8} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-8} \\\Leftrightarrow & 140x+42x& = & 21-8 \\\Leftrightarrow & \color{red}{182} x& = & 13 \\\Leftrightarrow & x = \frac{13}{182} & & \\\Leftrightarrow & x = \frac{1}{14} & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+160} & = & \color{red}{350x} +63 \\\Leftrightarrow & -840x \color{red}{+160} \color{blue}{-160} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{-160} \\\Leftrightarrow & -840x-350x& = & 63-160 \\\Leftrightarrow & \color{red}{-1190} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1190} & & \\\Leftrightarrow & x = \frac{97}{1190} & & \\ & V = \left\{ \frac{97}{1190} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-480}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -480x \color{red}{-48} & = & \color{red}{100x} +45 \\\Leftrightarrow & -480x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -480x-100x& = & 45+48 \\\Leftrightarrow & \color{red}{-580} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-580} & & \\\Leftrightarrow & x = \frac{-93}{580} & & \\ & V = \left\{ \frac{-93}{580} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+40} & = & \color{red}{105x} +24 \\\Leftrightarrow & -240x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & -240x-105x& = & 24-40 \\\Leftrightarrow & \color{red}{-345} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-345} & & \\\Leftrightarrow & x = \frac{16}{345} & & \\ & V = \left\{ \frac{16}{345} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{9}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+81} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{+81} \color{blue}{-81} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-81} \\\Leftrightarrow & -270x+315x& = & 50-81 \\\Leftrightarrow & \color{red}{45} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{45} & & \\ & V = \left\{ \frac{-31}{45} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{6})& = & 3x+\frac{9}{11} \\\Leftrightarrow & -35x-\frac{35}{6}& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-2310}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{198}{ \color{blue}{66} }x+ \frac{54}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -2310x \color{red}{-385} & = & \color{red}{198x} +54 \\\Leftrightarrow & -2310x \color{red}{-385} \color{blue}{+385} \color{blue}{-198x} & = & \color{red}{198x} +54 \color{blue}{-198x} \color{blue}{+385} \\\Leftrightarrow & -2310x-198x& = & 54+385 \\\Leftrightarrow & \color{red}{-2508} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-2508} & & \\\Leftrightarrow & x = \frac{-439}{2508} & & \\ & V = \left\{ \frac{-439}{2508} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{3})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{35}{3}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{-35} & = & \color{red}{-27x} +10 \\\Leftrightarrow & 42x \color{red}{-35} \color{blue}{+35} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{+35} \\\Leftrightarrow & 42x+27x& = & 10+35 \\\Leftrightarrow & \color{red}{69} x& = & 45 \\\Leftrightarrow & x = \frac{45}{69} & & \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{105x} +14 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 378x-105x& = & 14-90 \\\Leftrightarrow & \color{red}{273} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{273} & & \\ & V = \left\{ \frac{-76}{273} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x+ \frac{250}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{+250} & = & \color{red}{-270x} +81 \\\Leftrightarrow & -1800x \color{red}{+250} \color{blue}{-250} \color{blue}{+270x} & = & \color{red}{-270x} +81 \color{blue}{+270x} \color{blue}{-250} \\\Leftrightarrow & -1800x+270x& = & 81-250 \\\Leftrightarrow & \color{red}{-1530} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-1530} & & \\\Leftrightarrow & x = \frac{169}{1530} & & \\ & V = \left\{ \frac{169}{1530} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-140} & = & \color{red}{-105x} +27 \\\Leftrightarrow & -252x \color{red}{-140} \color{blue}{+140} \color{blue}{+105x} & = & \color{red}{-105x} +27 \color{blue}{+105x} \color{blue}{+140} \\\Leftrightarrow & -252x+105x& = & 27+140 \\\Leftrightarrow & \color{red}{-147} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-147} & & \\\Leftrightarrow & x = \frac{-167}{147} & & \\ & V = \left\{ \frac{-167}{147} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+330} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & 924x-385x& = & 42-330 \\\Leftrightarrow & \color{red}{539} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{539} & & \\ & V = \left\{ \frac{-288}{539} \right\} & \\\end{align}\)
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