Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 90x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 90x+75x& = & 10+36 \\\Leftrightarrow & \color{red}{165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{165} & & \\ & V = \left\{ \frac{46}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{3})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{150x} +9 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{-150x} & = & \color{red}{150x} +9 \color{blue}{-150x} \color{blue}{-140} \\\Leftrightarrow & -420x-150x& = & 9-140 \\\Leftrightarrow & \color{red}{-570} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-570} & & \\\Leftrightarrow & x = \frac{131}{570} & & \\ & V = \left\{ \frac{131}{570} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{-27x} +5 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{+27x} & = & \color{red}{-27x} +5 \color{blue}{+27x} \color{blue}{-35} \\\Leftrightarrow & -126x+27x& = & 5-35 \\\Leftrightarrow & \color{red}{-99} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{-99} & & \\\Leftrightarrow & x = \frac{10}{33} & & \\ & V = \left\{ \frac{10}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+216} & = & \color{red}{225x} +10 \\\Leftrightarrow & -1080x \color{red}{+216} \color{blue}{-216} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-216} \\\Leftrightarrow & -1080x-225x& = & 10-216 \\\Leftrightarrow & \color{red}{-1305} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{-1305} & & \\\Leftrightarrow & x = \frac{206}{1305} & & \\ & V = \left\{ \frac{206}{1305} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -30x-\frac{18}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{198}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-198} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -2310x \color{red}{-198} \color{blue}{+198} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+198} \\\Leftrightarrow & -2310x+539x& = & 35+198 \\\Leftrightarrow & \color{red}{-1771} x& = & 233 \\\Leftrightarrow & x = \frac{233}{-1771} & & \\\Leftrightarrow & x = \frac{-233}{1771} & & \\ & V = \left\{ \frac{-233}{1771} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+264} & = & \color{red}{385x} +30 \\\Leftrightarrow & -1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & -1650x-385x& = & 30-264 \\\Leftrightarrow & \color{red}{-2035} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{-2035} & & \\\Leftrightarrow & x = \frac{234}{2035} & & \\ & V = \left\{ \frac{234}{2035} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -35x+\frac{21}{10}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-350}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -350x \color{red}{+21} & = & \color{red}{-30x} +25 \\\Leftrightarrow & -350x \color{red}{+21} \color{blue}{-21} \color{blue}{+30x} & = & \color{red}{-30x} +25 \color{blue}{+30x} \color{blue}{-21} \\\Leftrightarrow & -350x+30x& = & 25-21 \\\Leftrightarrow & \color{red}{-320} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-320} & & \\\Leftrightarrow & x = \frac{-1}{80} & & \\ & V = \left\{ \frac{-1}{80} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -16x-\frac{20}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1760}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1760x \color{red}{-200} & = & \color{red}{770x} +77 \\\Leftrightarrow & -1760x \color{red}{-200} \color{blue}{+200} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{+200} \\\Leftrightarrow & -1760x-770x& = & 77+200 \\\Leftrightarrow & \color{red}{-2530} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-2530} & & \\\Leftrightarrow & x = \frac{-277}{2530} & & \\ & V = \left\{ \frac{-277}{2530} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{15}{2}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{-42x} +16 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{+42x} & = & \color{red}{-42x} +16 \color{blue}{+42x} \color{blue}{+45} \\\Leftrightarrow & 72x+42x& = & 16+45 \\\Leftrightarrow & \color{red}{114} x& = & 61 \\\Leftrightarrow & x = \frac{61}{114} & & \\ & V = \left\{ \frac{61}{114} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{9})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-100} & = & \color{red}{-360x} +72 \\\Leftrightarrow & -675x \color{red}{-100} \color{blue}{+100} \color{blue}{+360x} & = & \color{red}{-360x} +72 \color{blue}{+360x} \color{blue}{+100} \\\Leftrightarrow & -675x+360x& = & 72+100 \\\Leftrightarrow & \color{red}{-315} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-315} & & \\\Leftrightarrow & x = \frac{-172}{315} & & \\ & V = \left\{ \frac{-172}{315} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & -9x+\frac{7}{11} \\\Leftrightarrow & 14x-\frac{14}{11}& = & -9x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{154}{ \color{blue}{11} }x- \frac{14}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 154x \color{red}{-14} & = & \color{red}{-99x} +7 \\\Leftrightarrow & 154x \color{red}{-14} \color{blue}{+14} \color{blue}{+99x} & = & \color{red}{-99x} +7 \color{blue}{+99x} \color{blue}{+14} \\\Leftrightarrow & 154x+99x& = & 7+14 \\\Leftrightarrow & \color{red}{253} x& = & 21 \\\Leftrightarrow & x = \frac{21}{253} & & \\ & V = \left\{ \frac{21}{253} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+176} \\\Leftrightarrow & -1232x+539x& = & 14+176 \\\Leftrightarrow & \color{red}{-693} x& = & 190 \\\Leftrightarrow & x = \frac{190}{-693} & & \\\Leftrightarrow & x = \frac{-190}{693} & & \\ & V = \left\{ \frac{-190}{693} \right\} & \\\end{align}\)
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