Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+84} & = & \color{red}{245x} +50 \\\Leftrightarrow & -700x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -700x-245x& = & 50-84 \\\Leftrightarrow & \color{red}{-945} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-945} & & \\\Leftrightarrow & x = \frac{34}{945} & & \\ & V = \left\{ \frac{34}{945} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -120x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{-95} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-95} & & \\\Leftrightarrow & x = \frac{6}{95} & & \\ & V = \left\{ \frac{6}{95} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1680}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1680x \color{red}{-240} & = & \color{red}{-392x} +63 \\\Leftrightarrow & -1680x \color{red}{-240} \color{blue}{+240} \color{blue}{+392x} & = & \color{red}{-392x} +63 \color{blue}{+392x} \color{blue}{+240} \\\Leftrightarrow & -1680x+392x& = & 63+240 \\\Leftrightarrow & \color{red}{-1288} x& = & 303 \\\Leftrightarrow & x = \frac{303}{-1288} & & \\\Leftrightarrow & x = \frac{-303}{1288} & & \\ & V = \left\{ \frac{-303}{1288} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-36} & = & \color{red}{105x} +40 \\\Leftrightarrow & 225x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 225x-105x& = & 40+36 \\\Leftrightarrow & \color{red}{120} x& = & 76 \\\Leftrightarrow & x = \frac{76}{120} & & \\\Leftrightarrow & x = \frac{19}{30} & & \\ & V = \left\{ \frac{19}{30} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{5})& = & 2x+\frac{7}{9} \\\Leftrightarrow & 35x-\frac{21}{5}& = & 2x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1575}{ \color{blue}{45} }x- \frac{189}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1575x \color{red}{-189} & = & \color{red}{90x} +35 \\\Leftrightarrow & 1575x \color{red}{-189} \color{blue}{+189} \color{blue}{-90x} & = & \color{red}{90x} +35 \color{blue}{-90x} \color{blue}{+189} \\\Leftrightarrow & 1575x-90x& = & 35+189 \\\Leftrightarrow & \color{red}{1485} x& = & 224 \\\Leftrightarrow & x = \frac{224}{1485} & & \\ & V = \left\{ \frac{224}{1485} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+35} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -154x \color{red}{+35} \color{blue}{-35} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-35} \\\Leftrightarrow & -154x+55x& = & 6-35 \\\Leftrightarrow & \color{red}{-99} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-99} & & \\\Leftrightarrow & x = \frac{29}{99} & & \\ & V = \left\{ \frac{29}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -3x+\frac{6}{7} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+10} & = & \color{red}{-21x} +6 \\\Leftrightarrow & -56x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +6 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & -56x+21x& = & 6-10 \\\Leftrightarrow & \color{red}{-35} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-35} & & \\\Leftrightarrow & x = \frac{4}{35} & & \\ & V = \left\{ \frac{4}{35} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{385x} +110 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -1848x-385x& = & 110-126 \\\Leftrightarrow & \color{red}{-2233} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-2233} & & \\\Leftrightarrow & x = \frac{16}{2233} & & \\ & V = \left\{ \frac{16}{2233} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 12x-\frac{16}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1584}{ \color{blue}{132} }x- \frac{192}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1584x \color{red}{-192} & = & \color{red}{660x} +55 \\\Leftrightarrow & 1584x \color{red}{-192} \color{blue}{+192} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{+192} \\\Leftrightarrow & 1584x-660x& = & 55+192 \\\Leftrightarrow & \color{red}{924} x& = & 247 \\\Leftrightarrow & x = \frac{247}{924} & & \\ & V = \left\{ \frac{247}{924} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{12}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+36} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 528x \color{red}{+36} \color{blue}{-36} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{-36} \\\Leftrightarrow & 528x+297x& = & 44-36 \\\Leftrightarrow & \color{red}{825} x& = & 8 \\\Leftrightarrow & x = \frac{8}{825} & & \\ & V = \left\{ \frac{8}{825} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & 6x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{25}{11}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{175}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-175} & = & \color{red}{462x} +110 \\\Leftrightarrow & 1925x \color{red}{-175} \color{blue}{+175} \color{blue}{-462x} & = & \color{red}{462x} +110 \color{blue}{-462x} \color{blue}{+175} \\\Leftrightarrow & 1925x-462x& = & 110+175 \\\Leftrightarrow & \color{red}{1463} x& = & 285 \\\Leftrightarrow & x = \frac{285}{1463} & & \\\Leftrightarrow & x = \frac{15}{77} & & \\ & V = \left\{ \frac{15}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+100} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -300x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -300x+105x& = & 18-100 \\\Leftrightarrow & \color{red}{-195} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-195} & & \\\Leftrightarrow & x = \frac{82}{195} & & \\ & V = \left\{ \frac{82}{195} \right\} & \\\end{align}\)
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