Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{18}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{72}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+72} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{+72} \color{blue}{-72} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-72} \\\Leftrightarrow & -240x+100x& = & 45-72 \\\Leftrightarrow & \color{red}{-140} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-140} & & \\\Leftrightarrow & x = \frac{27}{140} & & \\ & V = \left\{ \frac{27}{140} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+27} & = & \color{red}{-150x} +40 \\\Leftrightarrow & -360x \color{red}{+27} \color{blue}{-27} \color{blue}{+150x} & = & \color{red}{-150x} +40 \color{blue}{+150x} \color{blue}{-27} \\\Leftrightarrow & -360x+150x& = & 40-27 \\\Leftrightarrow & \color{red}{-210} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-210} & & \\\Leftrightarrow & x = \frac{-13}{210} & & \\ & V = \left\{ \frac{-13}{210} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 28+18 \\\Leftrightarrow & \color{red}{21} x& = & 46 \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{-270x} +9 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{-80} \\\Leftrightarrow & 300x+270x& = & 9-80 \\\Leftrightarrow & \color{red}{570} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{570} & & \\ & V = \left\{ \frac{-71}{570} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{112}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{112x} +72 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{-112x} & = & \color{red}{112x} +72 \color{blue}{-112x} \color{blue}{+147} \\\Leftrightarrow & 1176x-112x& = & 72+147 \\\Leftrightarrow & \color{red}{1064} x& = & 219 \\\Leftrightarrow & x = \frac{219}{1064} & & \\ & V = \left\{ \frac{219}{1064} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+30} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -84x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & -84x+189x& = & 56-30 \\\Leftrightarrow & \color{red}{105} x& = & 26 \\\Leftrightarrow & x = \frac{26}{105} & & \\ & V = \left\{ \frac{26}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{9})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 20x-\frac{25}{9}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{50}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-50} & = & \color{red}{126x} +15 \\\Leftrightarrow & 360x \color{red}{-50} \color{blue}{+50} \color{blue}{-126x} & = & \color{red}{126x} +15 \color{blue}{-126x} \color{blue}{+50} \\\Leftrightarrow & 360x-126x& = & 15+50 \\\Leftrightarrow & \color{red}{234} x& = & 65 \\\Leftrightarrow & x = \frac{65}{234} & & \\\Leftrightarrow & x = \frac{5}{18} & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & 6x+\frac{7}{3} \\\Leftrightarrow & -35x-\frac{21}{11}& = & 6x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-63} & = & \color{red}{198x} +77 \\\Leftrightarrow & -1155x \color{red}{-63} \color{blue}{+63} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{+63} \\\Leftrightarrow & -1155x-198x& = & 77+63 \\\Leftrightarrow & \color{red}{-1353} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-1353} & & \\\Leftrightarrow & x = \frac{-140}{1353} & & \\ & V = \left\{ \frac{-140}{1353} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+40} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 420x \color{red}{+40} \color{blue}{-40} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-40} \\\Leftrightarrow & 420x+175x& = & 42-40 \\\Leftrightarrow & \color{red}{595} x& = & 2 \\\Leftrightarrow & x = \frac{2}{595} & & \\ & V = \left\{ \frac{2}{595} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 270x-75x& = & 20-36 \\\Leftrightarrow & \color{red}{195} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{195} & & \\ & V = \left\{ \frac{-16}{195} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 360x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{435} x& = & 14 \\\Leftrightarrow & x = \frac{14}{435} & & \\ & V = \left\{ \frac{14}{435} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-72x} +18 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+72x} & = & \color{red}{-72x} +18 \color{blue}{+72x} \color{blue}{-21} \\\Leftrightarrow & -224x+72x& = & 18-21 \\\Leftrightarrow & \color{red}{-152} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-152} & & \\\Leftrightarrow & x = \frac{3}{152} & & \\ & V = \left\{ \frac{3}{152} \right\} & \\\end{align}\)