Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+25} & = & \color{red}{24x} +36 \\\Leftrightarrow & 160x \color{red}{+25} \color{blue}{-25} \color{blue}{-24x} & = & \color{red}{24x} +36 \color{blue}{-24x} \color{blue}{-25} \\\Leftrightarrow & 160x-24x& = & 36-25 \\\Leftrightarrow & \color{red}{136} x& = & 11 \\\Leftrightarrow & x = \frac{11}{136} & & \\ & V = \left\{ \frac{11}{136} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+66} & = & \color{red}{693x} +42 \\\Leftrightarrow & -616x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & -616x-693x& = & 42-66 \\\Leftrightarrow & \color{red}{-1309} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-1309} & & \\\Leftrightarrow & x = \frac{24}{1309} & & \\ & V = \left\{ \frac{24}{1309} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+90} & = & \color{red}{189x} +28 \\\Leftrightarrow & -1260x \color{red}{+90} \color{blue}{-90} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-90} \\\Leftrightarrow & -1260x-189x& = & 28-90 \\\Leftrightarrow & \color{red}{-1449} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-1449} & & \\\Leftrightarrow & x = \frac{62}{1449} & & \\ & V = \left\{ \frac{62}{1449} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{2})& = & 2x+\frac{5}{9} \\\Leftrightarrow & -25x-\frac{25}{2}& = & 2x+\frac{5}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{10}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{-225} & = & \color{red}{36x} +10 \\\Leftrightarrow & -450x \color{red}{-225} \color{blue}{+225} \color{blue}{-36x} & = & \color{red}{36x} +10 \color{blue}{-36x} \color{blue}{+225} \\\Leftrightarrow & -450x-36x& = & 10+225 \\\Leftrightarrow & \color{red}{-486} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-486} & & \\\Leftrightarrow & x = \frac{-235}{486} & & \\ & V = \left\{ \frac{-235}{486} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{7})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+6} & = & \color{red}{28x} +10 \\\Leftrightarrow & -105x \color{red}{+6} \color{blue}{-6} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{-6} \\\Leftrightarrow & -105x-28x& = & 10-6 \\\Leftrightarrow & \color{red}{-133} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-133} & & \\\Leftrightarrow & x = \frac{-4}{133} & & \\ & V = \left\{ \frac{-4}{133} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{245x} +56 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-245x} & = & \color{red}{245x} +56 \color{blue}{-245x} \color{blue}{+100} \\\Leftrightarrow & 560x-245x& = & 56+100 \\\Leftrightarrow & \color{red}{315} x& = & 156 \\\Leftrightarrow & x = \frac{156}{315} & & \\\Leftrightarrow & x = \frac{52}{105} & & \\ & V = \left\{ \frac{52}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-110} & = & \color{red}{-231x} +21 \\\Leftrightarrow & -660x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +21 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -660x+231x& = & 21+110 \\\Leftrightarrow & \color{red}{-429} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-429} & & \\\Leftrightarrow & x = \frac{-131}{429} & & \\ & V = \left\{ \frac{-131}{429} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{-147x} +12 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & 168x+147x& = & 12+56 \\\Leftrightarrow & \color{red}{315} x& = & 68 \\\Leftrightarrow & x = \frac{68}{315} & & \\ & V = \left\{ \frac{68}{315} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{8}{3}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-40} & = & \color{red}{75x} +18 \\\Leftrightarrow & -60x \color{red}{-40} \color{blue}{+40} \color{blue}{-75x} & = & \color{red}{75x} +18 \color{blue}{-75x} \color{blue}{+40} \\\Leftrightarrow & -60x-75x& = & 18+40 \\\Leftrightarrow & \color{red}{-135} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-135} & & \\\Leftrightarrow & x = \frac{-58}{135} & & \\ & V = \left\{ \frac{-58}{135} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{-275x} +44 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{-90} \\\Leftrightarrow & 990x+275x& = & 44-90 \\\Leftrightarrow & \color{red}{1265} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{1265} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -4x-\frac{8}{3}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-56} & = & \color{red}{105x} +9 \\\Leftrightarrow & -84x \color{red}{-56} \color{blue}{+56} \color{blue}{-105x} & = & \color{red}{105x} +9 \color{blue}{-105x} \color{blue}{+56} \\\Leftrightarrow & -84x-105x& = & 9+56 \\\Leftrightarrow & \color{red}{-189} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-189} & & \\\Leftrightarrow & x = \frac{-65}{189} & & \\ & V = \left\{ \frac{-65}{189} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{9}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-27} \\\Leftrightarrow & 180x+105x& = & 50-27 \\\Leftrightarrow & \color{red}{285} x& = & 23 \\\Leftrightarrow & x = \frac{23}{285} & & \\ & V = \left\{ \frac{23}{285} \right\} & \\\end{align}\)
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