Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+44} & = & \color{red}{-165x} +10 \\\Leftrightarrow & 550x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +10 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & 550x+165x& = & 10-44 \\\Leftrightarrow & \color{red}{715} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{715} & & \\ & V = \left\{ \frac{-34}{715} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{280}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-280} & = & \color{red}{-270x} +21 \\\Leftrightarrow & 1050x \color{red}{-280} \color{blue}{+280} \color{blue}{+270x} & = & \color{red}{-270x} +21 \color{blue}{+270x} \color{blue}{+280} \\\Leftrightarrow & 1050x+270x& = & 21+280 \\\Leftrightarrow & \color{red}{1320} x& = & 301 \\\Leftrightarrow & x = \frac{301}{1320} & & \\ & V = \left\{ \frac{301}{1320} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 30x+\frac{30}{11}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+210} & = & \color{red}{539x} +66 \\\Leftrightarrow & 2310x \color{red}{+210} \color{blue}{-210} \color{blue}{-539x} & = & \color{red}{539x} +66 \color{blue}{-539x} \color{blue}{-210} \\\Leftrightarrow & 2310x-539x& = & 66-210 \\\Leftrightarrow & \color{red}{1771} x& = & -144 \\\Leftrightarrow & x = \frac{-144}{1771} & & \\ & V = \left\{ \frac{-144}{1771} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{9})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-288}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -288x \color{red}{+64} & = & \color{red}{-360x} +63 \\\Leftrightarrow & -288x \color{red}{+64} \color{blue}{-64} \color{blue}{+360x} & = & \color{red}{-360x} +63 \color{blue}{+360x} \color{blue}{-64} \\\Leftrightarrow & -288x+360x& = & 63-64 \\\Leftrightarrow & \color{red}{72} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{72} & & \\ & V = \left\{ \frac{-1}{72} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+8} & = & \color{red}{54x} +27 \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-54x} & = & \color{red}{54x} +27 \color{blue}{-54x} \color{blue}{-8} \\\Leftrightarrow & -24x-54x& = & 27-8 \\\Leftrightarrow & \color{red}{-78} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-78} & & \\\Leftrightarrow & x = \frac{-19}{78} & & \\ & V = \left\{ \frac{-19}{78} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{4}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+44} & = & \color{red}{231x} +30 \\\Leftrightarrow & -330x \color{red}{+44} \color{blue}{-44} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{-44} \\\Leftrightarrow & -330x-231x& = & 30-44 \\\Leftrightarrow & \color{red}{-561} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-561} & & \\\Leftrightarrow & x = \frac{14}{561} & & \\ & V = \left\{ \frac{14}{561} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+176} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -1540x \color{red}{+176} \color{blue}{-176} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-176} \\\Leftrightarrow & -1540x+539x& = & 42-176 \\\Leftrightarrow & \color{red}{-1001} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{-1001} & & \\\Leftrightarrow & x = \frac{134}{1001} & & \\ & V = \left\{ \frac{134}{1001} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-35} & = & \color{red}{27x} +2 \\\Leftrightarrow & -315x \color{red}{-35} \color{blue}{+35} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+35} \\\Leftrightarrow & -315x-27x& = & 2+35 \\\Leftrightarrow & \color{red}{-342} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-342} & & \\\Leftrightarrow & x = \frac{-37}{342} & & \\ & V = \left\{ \frac{-37}{342} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{9}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+27} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{+27} \color{blue}{-27} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-27} \\\Leftrightarrow & -252x+105x& = & 56-27 \\\Leftrightarrow & \color{red}{-147} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-147} & & \\\Leftrightarrow & x = \frac{-29}{147} & & \\ & V = \left\{ \frac{-29}{147} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+75} & = & \color{red}{80x} +6 \\\Leftrightarrow & -150x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +6 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & -150x-80x& = & 6-75 \\\Leftrightarrow & \color{red}{-230} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-230} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{10})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{9}{10}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{20}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{-27} & = & \color{red}{240x} +20 \\\Leftrightarrow & -450x \color{red}{-27} \color{blue}{+27} \color{blue}{-240x} & = & \color{red}{240x} +20 \color{blue}{-240x} \color{blue}{+27} \\\Leftrightarrow & -450x-240x& = & 20+27 \\\Leftrightarrow & \color{red}{-690} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-690} & & \\\Leftrightarrow & x = \frac{-47}{690} & & \\ & V = \left\{ \frac{-47}{690} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{150x} +9 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{-150x} & = & \color{red}{150x} +9 \color{blue}{-150x} \color{blue}{+80} \\\Leftrightarrow & 240x-150x& = & 9+80 \\\Leftrightarrow & \color{red}{90} x& = & 89 \\\Leftrightarrow & x = \frac{89}{90} & & \\ & V = \left\{ \frac{89}{90} \right\} & \\\end{align}\)
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