Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-110} & = & \color{red}{693x} +42 \\\Leftrightarrow & 1540x \color{red}{-110} \color{blue}{+110} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{+110} \\\Leftrightarrow & 1540x-693x& = & 42+110 \\\Leftrightarrow & \color{red}{847} x& = & 152 \\\Leftrightarrow & x = \frac{152}{847} & & \\ & V = \left\{ \frac{152}{847} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 108x \color{red}{-45} & = & \color{red}{24x} +10 \\\Leftrightarrow & 108x \color{red}{-45} \color{blue}{+45} \color{blue}{-24x} & = & \color{red}{24x} +10 \color{blue}{-24x} \color{blue}{+45} \\\Leftrightarrow & 108x-24x& = & 10+45 \\\Leftrightarrow & \color{red}{84} x& = & 55 \\\Leftrightarrow & x = \frac{55}{84} & & \\ & V = \left\{ \frac{55}{84} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+54} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -540x \color{red}{+54} \color{blue}{-54} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-54} \\\Leftrightarrow & -540x+225x& = & 10-54 \\\Leftrightarrow & \color{red}{-315} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-315} & & \\\Leftrightarrow & x = \frac{44}{315} & & \\ & V = \left\{ \frac{44}{315} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-60} \\\Leftrightarrow & -252x+105x& = & 70-60 \\\Leftrightarrow & \color{red}{-147} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-147} & & \\\Leftrightarrow & x = \frac{-10}{147} & & \\ & V = \left\{ \frac{-10}{147} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+72} & = & \color{red}{308x} +33 \\\Leftrightarrow & -1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & -1320x-308x& = & 33-72 \\\Leftrightarrow & \color{red}{-1628} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-1628} & & \\\Leftrightarrow & x = \frac{39}{1628} & & \\ & V = \left\{ \frac{39}{1628} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{630x} +63 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-630x} & = & \color{red}{630x} +63 \color{blue}{-630x} \color{blue}{+100} \\\Leftrightarrow & 700x-630x& = & 63+100 \\\Leftrightarrow & \color{red}{70} x& = & 163 \\\Leftrightarrow & x = \frac{163}{70} & & \\ & V = \left\{ \frac{163}{70} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{+140} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 1260x \color{red}{+140} \color{blue}{-140} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{-140} \\\Leftrightarrow & 1260x+225x& = & 54-140 \\\Leftrightarrow & \color{red}{1485} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{1485} & & \\ & V = \left\{ \frac{-86}{1485} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & 84x+70x& = & 21-12 \\\Leftrightarrow & \color{red}{154} x& = & 9 \\\Leftrightarrow & x = \frac{9}{154} & & \\ & V = \left\{ \frac{9}{154} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{10}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+40} & = & \color{red}{308x} +33 \\\Leftrightarrow & -264x \color{red}{+40} \color{blue}{-40} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{-40} \\\Leftrightarrow & -264x-308x& = & 33-40 \\\Leftrightarrow & \color{red}{-572} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-572} & & \\\Leftrightarrow & x = \frac{7}{572} & & \\ & V = \left\{ \frac{7}{572} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{11})& = & -9x+\frac{6}{7} \\\Leftrightarrow & 16x-\frac{16}{11}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-112} & = & \color{red}{-693x} +66 \\\Leftrightarrow & 1232x \color{red}{-112} \color{blue}{+112} \color{blue}{+693x} & = & \color{red}{-693x} +66 \color{blue}{+693x} \color{blue}{+112} \\\Leftrightarrow & 1232x+693x& = & 66+112 \\\Leftrightarrow & \color{red}{1925} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1925} & & \\ & V = \left\{ \frac{178}{1925} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{8})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{+15} & = & \color{red}{56x} +36 \\\Leftrightarrow & 120x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +36 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & 120x-56x& = & 36-15 \\\Leftrightarrow & \color{red}{64} x& = & 21 \\\Leftrightarrow & x = \frac{21}{64} & & \\ & V = \left\{ \frac{21}{64} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{4}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{16}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-16} & = & \color{red}{-196x} +21 \\\Leftrightarrow & -280x \color{red}{-16} \color{blue}{+16} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{+16} \\\Leftrightarrow & -280x+196x& = & 21+16 \\\Leftrightarrow & \color{red}{-84} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-84} & & \\\Leftrightarrow & x = \frac{-37}{84} & & \\ & V = \left\{ \frac{-37}{84} \right\} & \\\end{align}\)
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