Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{12}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+24} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -84x \color{red}{+24} \color{blue}{-24} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-24} \\\Leftrightarrow & -84x+98x& = & 35-24 \\\Leftrightarrow & \color{red}{14} x& = & 11 \\\Leftrightarrow & x = \frac{11}{14} & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-80} & = & \color{red}{168x} +49 \\\Leftrightarrow & -1120x \color{red}{-80} \color{blue}{+80} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{+80} \\\Leftrightarrow & -1120x-168x& = & 49+80 \\\Leftrightarrow & \color{red}{-1288} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-1288} & & \\\Leftrightarrow & x = \frac{-129}{1288} & & \\ & V = \left\{ \frac{-129}{1288} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +20 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 20+132 \\\Leftrightarrow & \color{red}{385} x& = & 152 \\\Leftrightarrow & x = \frac{152}{385} & & \\ & V = \left\{ \frac{152}{385} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{11})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 28x+\frac{21}{11}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+147} & = & \color{red}{231x} +22 \\\Leftrightarrow & 2156x \color{red}{+147} \color{blue}{-147} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-147} \\\Leftrightarrow & 2156x-231x& = & 22-147 \\\Leftrightarrow & \color{red}{1925} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1925} & & \\\Leftrightarrow & x = \frac{-5}{77} & & \\ & V = \left\{ \frac{-5}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{12x} +8 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +8 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & -84x-12x& = & 8+28 \\\Leftrightarrow & \color{red}{-96} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-96} & & \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 60x+70x& = & 45-24 \\\Leftrightarrow & \color{red}{130} x& = & 21 \\\Leftrightarrow & x = \frac{21}{130} & & \\ & V = \left\{ \frac{21}{130} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-140} & = & \color{red}{-441x} +27 \\\Leftrightarrow & -1008x \color{red}{-140} \color{blue}{+140} \color{blue}{+441x} & = & \color{red}{-441x} +27 \color{blue}{+441x} \color{blue}{+140} \\\Leftrightarrow & -1008x+441x& = & 27+140 \\\Leftrightarrow & \color{red}{-567} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-567} & & \\\Leftrightarrow & x = \frac{-167}{567} & & \\ & V = \left\{ \frac{-167}{567} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+180} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 1320x \color{red}{+180} \color{blue}{-180} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{-180} \\\Leftrightarrow & 1320x+550x& = & 33-180 \\\Leftrightarrow & \color{red}{1870} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{1870} & & \\ & V = \left\{ \frac{-147}{1870} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 21x+\frac{21}{11}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 231x \color{red}{+21} & = & \color{red}{55x} +4 \\\Leftrightarrow & 231x \color{red}{+21} \color{blue}{-21} \color{blue}{-55x} & = & \color{red}{55x} +4 \color{blue}{-55x} \color{blue}{-21} \\\Leftrightarrow & 231x-55x& = & 4-21 \\\Leftrightarrow & \color{red}{176} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{176} & & \\ & V = \left\{ \frac{-17}{176} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+132} & = & \color{red}{385x} +20 \\\Leftrightarrow & 1650x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1650x-385x& = & 20-132 \\\Leftrightarrow & \color{red}{1265} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{1265} & & \\ & V = \left\{ \frac{-112}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{-10} & = & \color{red}{77x} +10 \\\Leftrightarrow & -110x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & -110x-77x& = & 10+10 \\\Leftrightarrow & \color{red}{-187} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-187} & & \\\Leftrightarrow & x = \frac{-20}{187} & & \\ & V = \left\{ \frac{-20}{187} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 360x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{285} x& = & 4 \\\Leftrightarrow & x = \frac{4}{285} & & \\ & V = \left\{ \frac{4}{285} \right\} & \\\end{align}\)
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