Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1080}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1080x \color{red}{-108} & = & \color{red}{225x} +40 \\\Leftrightarrow & 1080x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & 1080x-225x& = & 40+108 \\\Leftrightarrow & \color{red}{855} x& = & 148 \\\Leftrightarrow & x = \frac{148}{855} & & \\ & V = \left\{ \frac{148}{855} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{21}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x- \frac{147}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{-147} & = & \color{red}{315x} +40 \\\Leftrightarrow & 490x \color{red}{-147} \color{blue}{+147} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+147} \\\Leftrightarrow & 490x-315x& = & 40+147 \\\Leftrightarrow & \color{red}{175} x& = & 187 \\\Leftrightarrow & x = \frac{187}{175} & & \\ & V = \left\{ \frac{187}{175} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & 2x+\frac{3}{7} \\\Leftrightarrow & 35x+\frac{35}{3}& = & 2x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+245} & = & \color{red}{42x} +9 \\\Leftrightarrow & 735x \color{red}{+245} \color{blue}{-245} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-245} \\\Leftrightarrow & 735x-42x& = & 9-245 \\\Leftrightarrow & \color{red}{693} x& = & -236 \\\Leftrightarrow & x = \frac{-236}{693} & & \\ & V = \left\{ \frac{-236}{693} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-105} & = & \color{red}{-392x} +80 \\\Leftrightarrow & 672x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +80 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & 672x+392x& = & 80+105 \\\Leftrightarrow & \color{red}{1064} x& = & 185 \\\Leftrightarrow & x = \frac{185}{1064} & & \\ & V = \left\{ \frac{185}{1064} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{5})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{90x} +45 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{-24} \\\Leftrightarrow & -80x-90x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+20} & = & \color{red}{-42x} +49 \\\Leftrightarrow & 56x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +49 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & 56x+42x& = & 49-20 \\\Leftrightarrow & \color{red}{98} x& = & 29 \\\Leftrightarrow & x = \frac{29}{98} & & \\ & V = \left\{ \frac{29}{98} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{2})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -14x-\frac{21}{2}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-231} & = & \color{red}{-110x} +20 \\\Leftrightarrow & -308x \color{red}{-231} \color{blue}{+231} \color{blue}{+110x} & = & \color{red}{-110x} +20 \color{blue}{+110x} \color{blue}{+231} \\\Leftrightarrow & -308x+110x& = & 20+231 \\\Leftrightarrow & \color{red}{-198} x& = & 251 \\\Leftrightarrow & x = \frac{251}{-198} & & \\\Leftrightarrow & x = \frac{-251}{198} & & \\ & V = \left\{ \frac{-251}{198} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{2})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 9x+\frac{15}{2}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+75} & = & \color{red}{70x} +3 \\\Leftrightarrow & 90x \color{red}{+75} \color{blue}{-75} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-75} \\\Leftrightarrow & 90x-70x& = & 3-75 \\\Leftrightarrow & \color{red}{20} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{20} & & \\\Leftrightarrow & x = \frac{-18}{5} & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{25}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+175} & = & \color{red}{539x} +88 \\\Leftrightarrow & 770x \color{red}{+175} \color{blue}{-175} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-175} \\\Leftrightarrow & 770x-539x& = & 88-175 \\\Leftrightarrow & \color{red}{231} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{231} & & \\\Leftrightarrow & x = \frac{-29}{77} & & \\ & V = \left\{ \frac{-29}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+10} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -28x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & -28x+63x& = & 10-10 \\\Leftrightarrow & \color{red}{35} x& = & 0 \\\Leftrightarrow & x = \frac{0}{35} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{105x} +56 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 378x-105x& = & 56-90 \\\Leftrightarrow & \color{red}{273} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{273} & & \\ & V = \left\{ \frac{-34}{273} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{3})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-140} & = & \color{red}{147x} +12 \\\Leftrightarrow & -336x \color{red}{-140} \color{blue}{+140} \color{blue}{-147x} & = & \color{red}{147x} +12 \color{blue}{-147x} \color{blue}{+140} \\\Leftrightarrow & -336x-147x& = & 12+140 \\\Leftrightarrow & \color{red}{-483} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-483} & & \\\Leftrightarrow & x = \frac{-152}{483} & & \\ & V = \left\{ \frac{-152}{483} \right\} & \\\end{align}\)
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