Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{-162} & = & \color{red}{-495x} +110 \\\Leftrightarrow & -2376x \color{red}{-162} \color{blue}{+162} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{+162} \\\Leftrightarrow & -2376x+495x& = & 110+162 \\\Leftrightarrow & \color{red}{-1881} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-1881} & & \\\Leftrightarrow & x = \frac{-272}{1881} & & \\ & V = \left\{ \frac{-272}{1881} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & 8x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 8x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{880}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-100} & = & \color{red}{880x} +77 \\\Leftrightarrow & -1650x \color{red}{-100} \color{blue}{+100} \color{blue}{-880x} & = & \color{red}{880x} +77 \color{blue}{-880x} \color{blue}{+100} \\\Leftrightarrow & -1650x-880x& = & 77+100 \\\Leftrightarrow & \color{red}{-2530} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-2530} & & \\\Leftrightarrow & x = \frac{-177}{2530} & & \\ & V = \left\{ \frac{-177}{2530} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+50} & = & \color{red}{175x} +21 \\\Leftrightarrow & -140x \color{red}{+50} \color{blue}{-50} \color{blue}{-175x} & = & \color{red}{175x} +21 \color{blue}{-175x} \color{blue}{-50} \\\Leftrightarrow & -140x-175x& = & 21-50 \\\Leftrightarrow & \color{red}{-315} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-315} & & \\\Leftrightarrow & x = \frac{29}{315} & & \\ & V = \left\{ \frac{29}{315} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 9x-\frac{6}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-42} & = & \color{red}{175x} +50 \\\Leftrightarrow & 315x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & 315x-175x& = & 50+42 \\\Leftrightarrow & \color{red}{140} x& = & 92 \\\Leftrightarrow & x = \frac{92}{140} & & \\\Leftrightarrow & x = \frac{23}{35} & & \\ & V = \left\{ \frac{23}{35} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{539x} +28 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1232x-539x& = & 28+176 \\\Leftrightarrow & \color{red}{-1771} x& = & 204 \\\Leftrightarrow & x = \frac{204}{-1771} & & \\\Leftrightarrow & x = \frac{-204}{1771} & & \\ & V = \left\{ \frac{-204}{1771} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 4x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{+135} & = & \color{red}{144x} +16 \\\Leftrightarrow & -540x \color{red}{+135} \color{blue}{-135} \color{blue}{-144x} & = & \color{red}{144x} +16 \color{blue}{-144x} \color{blue}{-135} \\\Leftrightarrow & -540x-144x& = & 16-135 \\\Leftrightarrow & \color{red}{-684} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-684} & & \\\Leftrightarrow & x = \frac{119}{684} & & \\ & V = \left\{ \frac{119}{684} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+150} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 1650x \color{red}{+150} \color{blue}{-150} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-150} \\\Leftrightarrow & 1650x+385x& = & 88-150 \\\Leftrightarrow & \color{red}{2035} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{2035} & & \\ & V = \left\{ \frac{-62}{2035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{9}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-99} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{-99} \color{blue}{+99} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+99} \\\Leftrightarrow & -660x-275x& = & 30+99 \\\Leftrightarrow & \color{red}{-935} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-935} & & \\\Leftrightarrow & x = \frac{-129}{935} & & \\ & V = \left\{ \frac{-129}{935} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & 6x+\frac{4}{7} \\\Leftrightarrow & 25x-\frac{20}{7}& = & 6x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{42}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-20} & = & \color{red}{42x} +4 \\\Leftrightarrow & 175x \color{red}{-20} \color{blue}{+20} \color{blue}{-42x} & = & \color{red}{42x} +4 \color{blue}{-42x} \color{blue}{+20} \\\Leftrightarrow & 175x-42x& = & 4+20 \\\Leftrightarrow & \color{red}{133} x& = & 24 \\\Leftrightarrow & x = \frac{24}{133} & & \\ & V = \left\{ \frac{24}{133} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{10})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -35x-\frac{21}{10}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-3150}{ \color{blue}{90} }x- \frac{189}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -3150x \color{red}{-189} & = & \color{red}{270x} +40 \\\Leftrightarrow & -3150x \color{red}{-189} \color{blue}{+189} \color{blue}{-270x} & = & \color{red}{270x} +40 \color{blue}{-270x} \color{blue}{+189} \\\Leftrightarrow & -3150x-270x& = & 40+189 \\\Leftrightarrow & \color{red}{-3420} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-3420} & & \\\Leftrightarrow & x = \frac{-229}{3420} & & \\ & V = \left\{ \frac{-229}{3420} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{891x} +44 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{-891x} & = & \color{red}{891x} +44 \color{blue}{-891x} \color{blue}{-90} \\\Leftrightarrow & 990x-891x& = & 44-90 \\\Leftrightarrow & \color{red}{99} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{99} & & \\ & V = \left\{ \frac{-46}{99} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 28+66 \\\Leftrightarrow & \color{red}{77} x& = & 94 \\\Leftrightarrow & x = \frac{94}{77} & & \\ & V = \left\{ \frac{94}{77} \right\} & \\\end{align}\)
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