Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+10} \\\Leftrightarrow & -28x+35x& = & 8+10 \\\Leftrightarrow & \color{red}{7} x& = & 18 \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{75x} +40 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 270x-75x& = & 40+72 \\\Leftrightarrow & \color{red}{195} x& = & 112 \\\Leftrightarrow & x = \frac{112}{195} & & \\ & V = \left\{ \frac{112}{195} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+28} & = & \color{red}{-30x} +7 \\\Leftrightarrow & -84x \color{red}{+28} \color{blue}{-28} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{-28} \\\Leftrightarrow & -84x+30x& = & 7-28 \\\Leftrightarrow & \color{red}{-54} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-54} & & \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{96x} +16 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{-96x} & = & \color{red}{96x} +16 \color{blue}{-96x} \color{blue}{+45} \\\Leftrightarrow & 180x-96x& = & 16+45 \\\Leftrightarrow & \color{red}{84} x& = & 61 \\\Leftrightarrow & x = \frac{61}{84} & & \\ & V = \left\{ \frac{61}{84} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{3})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+80} & = & \color{red}{150x} +9 \\\Leftrightarrow & -360x \color{red}{+80} \color{blue}{-80} \color{blue}{-150x} & = & \color{red}{150x} +9 \color{blue}{-150x} \color{blue}{-80} \\\Leftrightarrow & -360x-150x& = & 9-80 \\\Leftrightarrow & \color{red}{-510} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-510} & & \\\Leftrightarrow & x = \frac{71}{510} & & \\ & V = \left\{ \frac{71}{510} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -210x+147x& = & 70-30 \\\Leftrightarrow & \color{red}{-63} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-63} & & \\\Leftrightarrow & x = \frac{-40}{63} & & \\ & V = \left\{ \frac{-40}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{252}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 252x \color{red}{-36} & = & \color{red}{-210x} +49 \\\Leftrightarrow & 252x \color{red}{-36} \color{blue}{+36} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+36} \\\Leftrightarrow & 252x+210x& = & 49+36 \\\Leftrightarrow & \color{red}{462} x& = & 85 \\\Leftrightarrow & x = \frac{85}{462} & & \\ & V = \left\{ \frac{85}{462} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{8}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{80}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-80} & = & \color{red}{-550x} +33 \\\Leftrightarrow & -1320x \color{red}{-80} \color{blue}{+80} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{+80} \\\Leftrightarrow & -1320x+550x& = & 33+80 \\\Leftrightarrow & \color{red}{-770} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-770} & & \\\Leftrightarrow & x = \frac{-113}{770} & & \\ & V = \left\{ \frac{-113}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{11})& = & 8x+\frac{6}{7} \\\Leftrightarrow & -15x+\frac{15}{11}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+105} & = & \color{red}{616x} +66 \\\Leftrightarrow & -1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-616x} & = & \color{red}{616x} +66 \color{blue}{-616x} \color{blue}{-105} \\\Leftrightarrow & -1155x-616x& = & 66-105 \\\Leftrightarrow & \color{red}{-1771} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-1771} & & \\\Leftrightarrow & x = \frac{39}{1771} & & \\ & V = \left\{ \frac{39}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{11})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -14x-\frac{28}{11}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x- \frac{28}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{-28} & = & \color{red}{33x} +2 \\\Leftrightarrow & -154x \color{red}{-28} \color{blue}{+28} \color{blue}{-33x} & = & \color{red}{33x} +2 \color{blue}{-33x} \color{blue}{+28} \\\Leftrightarrow & -154x-33x& = & 2+28 \\\Leftrightarrow & \color{red}{-187} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-187} & & \\\Leftrightarrow & x = \frac{-30}{187} & & \\ & V = \left\{ \frac{-30}{187} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 9x+\frac{4}{7} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{189x} +12 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +12 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & 168x-189x& = & 12-28 \\\Leftrightarrow & \color{red}{-21} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-21} & & \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{9}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-9} & = & \color{red}{-25x} +2 \\\Leftrightarrow & -60x \color{red}{-9} \color{blue}{+9} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{+9} \\\Leftrightarrow & -60x+25x& = & 2+9 \\\Leftrightarrow & \color{red}{-35} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-35} & & \\\Leftrightarrow & x = \frac{-11}{35} & & \\ & V = \left\{ \frac{-11}{35} \right\} & \\\end{align}\)