Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+225} & = & \color{red}{126x} +20 \\\Leftrightarrow & -180x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +20 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & -180x-126x& = & 20-225 \\\Leftrightarrow & \color{red}{-306} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-306} & & \\\Leftrightarrow & x = \frac{205}{306} & & \\ & V = \left\{ \frac{205}{306} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{11})& = & 8x+\frac{9}{7} \\\Leftrightarrow & -21x-\frac{21}{11}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{-147} & = & \color{red}{616x} +99 \\\Leftrightarrow & -1617x \color{red}{-147} \color{blue}{+147} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{+147} \\\Leftrightarrow & -1617x-616x& = & 99+147 \\\Leftrightarrow & \color{red}{-2233} x& = & 246 \\\Leftrightarrow & x = \frac{246}{-2233} & & \\\Leftrightarrow & x = \frac{-246}{2233} & & \\ & V = \left\{ \frac{-246}{2233} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{4})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-75} & = & \color{red}{160x} +18 \\\Leftrightarrow & -300x \color{red}{-75} \color{blue}{+75} \color{blue}{-160x} & = & \color{red}{160x} +18 \color{blue}{-160x} \color{blue}{+75} \\\Leftrightarrow & -300x-160x& = & 18+75 \\\Leftrightarrow & \color{red}{-460} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-460} & & \\\Leftrightarrow & x = \frac{-93}{460} & & \\ & V = \left\{ \frac{-93}{460} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{7})& = & -2x+\frac{5}{4} \\\Leftrightarrow & 25x-\frac{10}{7}& = & -2x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-40} & = & \color{red}{-56x} +35 \\\Leftrightarrow & 700x \color{red}{-40} \color{blue}{+40} \color{blue}{+56x} & = & \color{red}{-56x} +35 \color{blue}{+56x} \color{blue}{+40} \\\Leftrightarrow & 700x+56x& = & 35+40 \\\Leftrightarrow & \color{red}{756} x& = & 75 \\\Leftrightarrow & x = \frac{75}{756} & & \\\Leftrightarrow & x = \frac{25}{252} & & \\ & V = \left\{ \frac{25}{252} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 16x+\frac{8}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{+8} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 112x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & 112x+35x& = & 10-8 \\\Leftrightarrow & \color{red}{147} x& = & 2 \\\Leftrightarrow & x = \frac{2}{147} & & \\ & V = \left\{ \frac{2}{147} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-224}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -224x \color{red}{-80} & = & \color{red}{280x} +63 \\\Leftrightarrow & -224x \color{red}{-80} \color{blue}{+80} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{+80} \\\Leftrightarrow & -224x-280x& = & 63+80 \\\Leftrightarrow & \color{red}{-504} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-504} & & \\\Leftrightarrow & x = \frac{-143}{504} & & \\ & V = \left\{ \frac{-143}{504} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{-72} & = & \color{red}{308x} +99 \\\Leftrightarrow & -1320x \color{red}{-72} \color{blue}{+72} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+72} \\\Leftrightarrow & -1320x-308x& = & 99+72 \\\Leftrightarrow & \color{red}{-1628} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-1628} & & \\\Leftrightarrow & x = \frac{-171}{1628} & & \\ & V = \left\{ \frac{-171}{1628} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{16}{11}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+112} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 616x \color{red}{+112} \color{blue}{-112} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-112} \\\Leftrightarrow & 616x+231x& = & 110-112 \\\Leftrightarrow & \color{red}{847} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{847} & & \\ & V = \left\{ \frac{-2}{847} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{20}{11}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+60} & = & \color{red}{-99x} +110 \\\Leftrightarrow & 330x \color{red}{+60} \color{blue}{-60} \color{blue}{+99x} & = & \color{red}{-99x} +110 \color{blue}{+99x} \color{blue}{-60} \\\Leftrightarrow & 330x+99x& = & 110-60 \\\Leftrightarrow & \color{red}{429} x& = & 50 \\\Leftrightarrow & x = \frac{50}{429} & & \\ & V = \left\{ \frac{50}{429} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{4})& = & -8x+\frac{10}{11} \\\Leftrightarrow & 35x+\frac{21}{4}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1540}{ \color{blue}{44} }x+ \frac{231}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1540x \color{red}{+231} & = & \color{red}{-352x} +40 \\\Leftrightarrow & 1540x \color{red}{+231} \color{blue}{-231} \color{blue}{+352x} & = & \color{red}{-352x} +40 \color{blue}{+352x} \color{blue}{-231} \\\Leftrightarrow & 1540x+352x& = & 40-231 \\\Leftrightarrow & \color{red}{1892} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{1892} & & \\ & V = \left\{ \frac{-191}{1892} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{3})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 28x+\frac{7}{3}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+21} & = & \color{red}{81x} +8 \\\Leftrightarrow & 252x \color{red}{+21} \color{blue}{-21} \color{blue}{-81x} & = & \color{red}{81x} +8 \color{blue}{-81x} \color{blue}{-21} \\\Leftrightarrow & 252x-81x& = & 8-21 \\\Leftrightarrow & \color{red}{171} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{171} & & \\ & V = \left\{ \frac{-13}{171} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{5})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -28x-\frac{21}{5}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{231}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-231} & = & \color{red}{440x} +25 \\\Leftrightarrow & -1540x \color{red}{-231} \color{blue}{+231} \color{blue}{-440x} & = & \color{red}{440x} +25 \color{blue}{-440x} \color{blue}{+231} \\\Leftrightarrow & -1540x-440x& = & 25+231 \\\Leftrightarrow & \color{red}{-1980} x& = & 256 \\\Leftrightarrow & x = \frac{256}{-1980} & & \\\Leftrightarrow & x = \frac{-64}{495} & & \\ & V = \left\{ \frac{-64}{495} \right\} & \\\end{align}\)
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