Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{3})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+80} & = & \color{red}{150x} +27 \\\Leftrightarrow & -360x \color{red}{+80} \color{blue}{-80} \color{blue}{-150x} & = & \color{red}{150x} +27 \color{blue}{-150x} \color{blue}{-80} \\\Leftrightarrow & -360x-150x& = & 27-80 \\\Leftrightarrow & \color{red}{-510} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-510} & & \\\Leftrightarrow & x = \frac{53}{510} & & \\ & V = \left\{ \frac{53}{510} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{60x} +21 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{-60x} & = & \color{red}{60x} +21 \color{blue}{-60x} \color{blue}{-56} \\\Leftrightarrow & 168x-60x& = & 21-56 \\\Leftrightarrow & \color{red}{108} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{108} & & \\ & V = \left\{ \frac{-35}{108} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{12x} +5 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +5 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & 126x-12x& = & 5+28 \\\Leftrightarrow & \color{red}{114} x& = & 33 \\\Leftrightarrow & x = \frac{33}{114} & & \\\Leftrightarrow & x = \frac{11}{38} & & \\ & V = \left\{ \frac{11}{38} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-18} & = & \color{red}{120x} +10 \\\Leftrightarrow & -225x \color{red}{-18} \color{blue}{+18} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{+18} \\\Leftrightarrow & -225x-120x& = & 10+18 \\\Leftrightarrow & \color{red}{-345} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-345} & & \\\Leftrightarrow & x = \frac{-28}{345} & & \\ & V = \left\{ \frac{-28}{345} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{35x} +6 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+10} \\\Leftrightarrow & -28x-35x& = & 6+10 \\\Leftrightarrow & \color{red}{-63} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-63} & & \\\Leftrightarrow & x = \frac{-16}{63} & & \\ & V = \left\{ \frac{-16}{63} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{3})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-100} & = & \color{red}{-105x} +9 \\\Leftrightarrow & 300x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +9 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & 300x+105x& = & 9+100 \\\Leftrightarrow & \color{red}{405} x& = & 109 \\\Leftrightarrow & x = \frac{109}{405} & & \\ & V = \left\{ \frac{109}{405} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{12})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{25}{12}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-2640}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{24}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -2640x \color{red}{-275} & = & \color{red}{-1188x} +24 \\\Leftrightarrow & -2640x \color{red}{-275} \color{blue}{+275} \color{blue}{+1188x} & = & \color{red}{-1188x} +24 \color{blue}{+1188x} \color{blue}{+275} \\\Leftrightarrow & -2640x+1188x& = & 24+275 \\\Leftrightarrow & \color{red}{-1452} x& = & 299 \\\Leftrightarrow & x = \frac{299}{-1452} & & \\\Leftrightarrow & x = \frac{-299}{1452} & & \\ & V = \left\{ \frac{-299}{1452} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+54} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 792x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & 792x+231x& = & 44-54 \\\Leftrightarrow & \color{red}{1023} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{1023} & & \\ & V = \left\{ \frac{-10}{1023} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{-15x} +8 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-20} \\\Leftrightarrow & -36x+15x& = & 8-20 \\\Leftrightarrow & \color{red}{-21} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-21} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{3})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+88} & = & \color{red}{231x} +27 \\\Leftrightarrow & 396x \color{red}{+88} \color{blue}{-88} \color{blue}{-231x} & = & \color{red}{231x} +27 \color{blue}{-231x} \color{blue}{-88} \\\Leftrightarrow & 396x-231x& = & 27-88 \\\Leftrightarrow & \color{red}{165} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{165} & & \\ & V = \left\{ \frac{-61}{165} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{11})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{231x} +55 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & -330x-231x& = & 55-30 \\\Leftrightarrow & \color{red}{-561} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-561} & & \\\Leftrightarrow & x = \frac{-25}{561} & & \\ & V = \left\{ \frac{-25}{561} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+40} & = & \color{red}{56x} +21 \\\Leftrightarrow & 700x \color{red}{+40} \color{blue}{-40} \color{blue}{-56x} & = & \color{red}{56x} +21 \color{blue}{-56x} \color{blue}{-40} \\\Leftrightarrow & 700x-56x& = & 21-40 \\\Leftrightarrow & \color{red}{644} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{644} & & \\ & V = \left\{ \frac{-19}{644} \right\} & \\\end{align}\)
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