Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 4x+\frac{8}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+88} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 220x \color{red}{+88} \color{blue}{-88} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{-88} \\\Leftrightarrow & 220x+385x& = & 30-88 \\\Leftrightarrow & \color{red}{605} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{605} & & \\ & V = \left\{ \frac{-58}{605} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{7})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{20}{7}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+80} & = & \color{red}{56x} +21 \\\Leftrightarrow & 420x \color{red}{+80} \color{blue}{-80} \color{blue}{-56x} & = & \color{red}{56x} +21 \color{blue}{-56x} \color{blue}{-80} \\\Leftrightarrow & 420x-56x& = & 21-80 \\\Leftrightarrow & \color{red}{364} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{364} & & \\ & V = \left\{ \frac{-59}{364} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{7})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+12} & = & \color{red}{-126x} +49 \\\Leftrightarrow & -112x \color{red}{+12} \color{blue}{-12} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{-12} \\\Leftrightarrow & -112x+126x& = & 49-12 \\\Leftrightarrow & \color{red}{14} x& = & 37 \\\Leftrightarrow & x = \frac{37}{14} & & \\ & V = \left\{ \frac{37}{14} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{11})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -4x-\frac{4}{11}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{20}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-20} & = & \color{red}{-275x} +22 \\\Leftrightarrow & -220x \color{red}{-20} \color{blue}{+20} \color{blue}{+275x} & = & \color{red}{-275x} +22 \color{blue}{+275x} \color{blue}{+20} \\\Leftrightarrow & -220x+275x& = & 22+20 \\\Leftrightarrow & \color{red}{55} x& = & 42 \\\Leftrightarrow & x = \frac{42}{55} & & \\ & V = \left\{ \frac{42}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-30} & = & \color{red}{63x} +56 \\\Leftrightarrow & 168x \color{red}{-30} \color{blue}{+30} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{+30} \\\Leftrightarrow & 168x-63x& = & 56+30 \\\Leftrightarrow & \color{red}{105} x& = & 86 \\\Leftrightarrow & x = \frac{86}{105} & & \\ & V = \left\{ \frac{86}{105} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & -4x+\frac{3}{10} \\\Leftrightarrow & 9x-\frac{6}{5}& = & -4x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{-40x} +3 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{+40x} & = & \color{red}{-40x} +3 \color{blue}{+40x} \color{blue}{+12} \\\Leftrightarrow & 90x+40x& = & 3+12 \\\Leftrightarrow & \color{red}{130} x& = & 15 \\\Leftrightarrow & x = \frac{15}{130} & & \\\Leftrightarrow & x = \frac{3}{26} & & \\ & V = \left\{ \frac{3}{26} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+36} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{+36} \color{blue}{-36} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-36} \\\Leftrightarrow & -396x-165x& = & 88-36 \\\Leftrightarrow & \color{red}{-561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-561} & & \\\Leftrightarrow & x = \frac{-52}{561} & & \\ & V = \left\{ \frac{-52}{561} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x+ \frac{240}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{+240} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 1980x \color{red}{+240} \color{blue}{-240} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{-240} \\\Leftrightarrow & 1980x+550x& = & 33-240 \\\Leftrightarrow & \color{red}{2530} x& = & -207 \\\Leftrightarrow & x = \frac{-207}{2530} & & \\\Leftrightarrow & x = \frac{-9}{110} & & \\ & V = \left\{ \frac{-9}{110} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & -4x+\frac{5}{12} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -4x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-80} & = & \color{red}{-48x} +5 \\\Leftrightarrow & 300x \color{red}{-80} \color{blue}{+80} \color{blue}{+48x} & = & \color{red}{-48x} +5 \color{blue}{+48x} \color{blue}{+80} \\\Leftrightarrow & 300x+48x& = & 5+80 \\\Leftrightarrow & \color{red}{348} x& = & 85 \\\Leftrightarrow & x = \frac{85}{348} & & \\ & V = \left\{ \frac{85}{348} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{25}{2}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-125} & = & \color{red}{-90x} +8 \\\Leftrightarrow & -200x \color{red}{-125} \color{blue}{+125} \color{blue}{+90x} & = & \color{red}{-90x} +8 \color{blue}{+90x} \color{blue}{+125} \\\Leftrightarrow & -200x+90x& = & 8+125 \\\Leftrightarrow & \color{red}{-110} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-110} & & \\\Leftrightarrow & x = \frac{-133}{110} & & \\ & V = \left\{ \frac{-133}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-63} & = & \color{red}{280x} +30 \\\Leftrightarrow & 315x \color{red}{-63} \color{blue}{+63} \color{blue}{-280x} & = & \color{red}{280x} +30 \color{blue}{-280x} \color{blue}{+63} \\\Leftrightarrow & 315x-280x& = & 30+63 \\\Leftrightarrow & \color{red}{35} x& = & 93 \\\Leftrightarrow & x = \frac{93}{35} & & \\ & V = \left\{ \frac{93}{35} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -8x+\frac{5}{12} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -8x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1512}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{-672}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1512x \color{red}{-360} & = & \color{red}{-672x} +35 \\\Leftrightarrow & -1512x \color{red}{-360} \color{blue}{+360} \color{blue}{+672x} & = & \color{red}{-672x} +35 \color{blue}{+672x} \color{blue}{+360} \\\Leftrightarrow & -1512x+672x& = & 35+360 \\\Leftrightarrow & \color{red}{-840} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-840} & & \\\Leftrightarrow & x = \frac{-79}{168} & & \\ & V = \left\{ \frac{-79}{168} \right\} & \\\end{align}\)
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