Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{8})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{9}{8}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{48}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 48x \color{red}{+9} & = & \color{red}{-40x} +36 \\\Leftrightarrow & 48x \color{red}{+9} \color{blue}{-9} \color{blue}{+40x} & = & \color{red}{-40x} +36 \color{blue}{+40x} \color{blue}{-9} \\\Leftrightarrow & 48x+40x& = & 36-9 \\\Leftrightarrow & \color{red}{88} x& = & 27 \\\Leftrightarrow & x = \frac{27}{88} & & \\ & V = \left\{ \frac{27}{88} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{16}{3}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+176} & = & \color{red}{99x} +12 \\\Leftrightarrow & 660x \color{red}{+176} \color{blue}{-176} \color{blue}{-99x} & = & \color{red}{99x} +12 \color{blue}{-99x} \color{blue}{-176} \\\Leftrightarrow & 660x-99x& = & 12-176 \\\Leftrightarrow & \color{red}{561} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{561} & & \\ & V = \left\{ \frac{-164}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{9})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{20}{9}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{-126x} +45 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{-40} \\\Leftrightarrow & 360x+126x& = & 45-40 \\\Leftrightarrow & \color{red}{486} x& = & 5 \\\Leftrightarrow & x = \frac{5}{486} & & \\ & V = \left\{ \frac{5}{486} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{231x} +88 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-72} \\\Leftrightarrow & -792x-231x& = & 88-72 \\\Leftrightarrow & \color{red}{-1023} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-1023} & & \\\Leftrightarrow & x = \frac{-16}{1023} & & \\ & V = \left\{ \frac{-16}{1023} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & -5x+\frac{5}{4} \\\Leftrightarrow & -14x+\frac{28}{3}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x+ \frac{112}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{+112} & = & \color{red}{-60x} +15 \\\Leftrightarrow & -168x \color{red}{+112} \color{blue}{-112} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{-112} \\\Leftrightarrow & -168x+60x& = & 15-112 \\\Leftrightarrow & \color{red}{-108} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-108} & & \\\Leftrightarrow & x = \frac{97}{108} & & \\ & V = \left\{ \frac{97}{108} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{2})& = & -2x+\frac{3}{5} \\\Leftrightarrow & 21x-\frac{21}{2}& = & -2x+\frac{3}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-105} & = & \color{red}{-20x} +6 \\\Leftrightarrow & 210x \color{red}{-105} \color{blue}{+105} \color{blue}{+20x} & = & \color{red}{-20x} +6 \color{blue}{+20x} \color{blue}{+105} \\\Leftrightarrow & 210x+20x& = & 6+105 \\\Leftrightarrow & \color{red}{230} x& = & 111 \\\Leftrightarrow & x = \frac{111}{230} & & \\ & V = \left\{ \frac{111}{230} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{-231x} +28 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & 770x+231x& = & 28+110 \\\Leftrightarrow & \color{red}{1001} x& = & 138 \\\Leftrightarrow & x = \frac{138}{1001} & & \\ & V = \left\{ \frac{138}{1001} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & 4x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{6}{5}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+66} & = & \color{red}{220x} +35 \\\Leftrightarrow & 825x \color{red}{+66} \color{blue}{-66} \color{blue}{-220x} & = & \color{red}{220x} +35 \color{blue}{-220x} \color{blue}{-66} \\\Leftrightarrow & 825x-220x& = & 35-66 \\\Leftrightarrow & \color{red}{605} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{605} & & \\ & V = \left\{ \frac{-31}{605} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 9x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+30} & = & \color{red}{495x} +44 \\\Leftrightarrow & 550x \color{red}{+30} \color{blue}{-30} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{-30} \\\Leftrightarrow & 550x-495x& = & 44-30 \\\Leftrightarrow & \color{red}{55} x& = & 14 \\\Leftrightarrow & x = \frac{14}{55} & & \\ & V = \left\{ \frac{14}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{42x} +21 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{-60} \\\Leftrightarrow & -252x-42x& = & 21-60 \\\Leftrightarrow & \color{red}{-294} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-294} & & \\\Leftrightarrow & x = \frac{13}{98} & & \\ & V = \left\{ \frac{13}{98} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{21}{4}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{700}{ \color{blue}{20} }x- \frac{105}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{160x} +24 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{-160x} & = & \color{red}{160x} +24 \color{blue}{-160x} \color{blue}{+105} \\\Leftrightarrow & 700x-160x& = & 24+105 \\\Leftrightarrow & \color{red}{540} x& = & 129 \\\Leftrightarrow & x = \frac{129}{540} & & \\\Leftrightarrow & x = \frac{43}{180} & & \\ & V = \left\{ \frac{43}{180} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 10x+\frac{15}{2}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+75} & = & \color{red}{-70x} +18 \\\Leftrightarrow & 100x \color{red}{+75} \color{blue}{-75} \color{blue}{+70x} & = & \color{red}{-70x} +18 \color{blue}{+70x} \color{blue}{-75} \\\Leftrightarrow & 100x+70x& = & 18-75 \\\Leftrightarrow & \color{red}{170} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{170} & & \\ & V = \left\{ \frac{-57}{170} \right\} & \\\end{align}\)
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