Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{2})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{21}{2}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-42}{ \color{blue}{2} }x- \frac{21}{ \color{blue}{2} })& = & (\frac{-16}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -42x \color{red}{-21} & = & \color{red}{-16x} +5 \\\Leftrightarrow & -42x \color{red}{-21} \color{blue}{+21} \color{blue}{+16x} & = & \color{red}{-16x} +5 \color{blue}{+16x} \color{blue}{+21} \\\Leftrightarrow & -42x+16x& = & 5+21 \\\Leftrightarrow & \color{red}{-26} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-26} & & \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -25x-\frac{15}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-15} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -175x \color{red}{-15} \color{blue}{+15} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+15} \\\Leftrightarrow & -175x+63x& = & 4+15 \\\Leftrightarrow & \color{red}{-112} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-112} & & \\\Leftrightarrow & x = \frac{-19}{112} & & \\ & V = \left\{ \frac{-19}{112} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{6})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 35x+\frac{35}{6}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{+175} & = & \color{red}{120x} +36 \\\Leftrightarrow & 1050x \color{red}{+175} \color{blue}{-175} \color{blue}{-120x} & = & \color{red}{120x} +36 \color{blue}{-120x} \color{blue}{-175} \\\Leftrightarrow & 1050x-120x& = & 36-175 \\\Leftrightarrow & \color{red}{930} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{930} & & \\ & V = \left\{ \frac{-139}{930} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{+21} & = & \color{red}{-24x} +36 \\\Leftrightarrow & 280x \color{red}{+21} \color{blue}{-21} \color{blue}{+24x} & = & \color{red}{-24x} +36 \color{blue}{+24x} \color{blue}{-21} \\\Leftrightarrow & 280x+24x& = & 36-21 \\\Leftrightarrow & \color{red}{304} x& = & 15 \\\Leftrightarrow & x = \frac{15}{304} & & \\ & V = \left\{ \frac{15}{304} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{8}{3}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{+8} & = & \color{red}{15x} +2 \\\Leftrightarrow & 18x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & 18x-15x& = & 2-8 \\\Leftrightarrow & \color{red}{3} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{3} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 14x-\frac{21}{8}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-21} & = & \color{red}{-40x} +18 \\\Leftrightarrow & 112x \color{red}{-21} \color{blue}{+21} \color{blue}{+40x} & = & \color{red}{-40x} +18 \color{blue}{+40x} \color{blue}{+21} \\\Leftrightarrow & 112x+40x& = & 18+21 \\\Leftrightarrow & \color{red}{152} x& = & 39 \\\Leftrightarrow & x = \frac{39}{152} & & \\ & V = \left\{ \frac{39}{152} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{15}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+45} & = & \color{red}{63x} +28 \\\Leftrightarrow & 420x \color{red}{+45} \color{blue}{-45} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-45} \\\Leftrightarrow & 420x-63x& = & 28-45 \\\Leftrightarrow & \color{red}{357} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{357} & & \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{550x} +33 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+120} \\\Leftrightarrow & 1320x-550x& = & 33+120 \\\Leftrightarrow & \color{red}{770} x& = & 153 \\\Leftrightarrow & x = \frac{153}{770} & & \\ & V = \left\{ \frac{153}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{-175x} +45 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{+42} \\\Leftrightarrow & 210x+175x& = & 45+42 \\\Leftrightarrow & \color{red}{385} x& = & 87 \\\Leftrightarrow & x = \frac{87}{385} & & \\ & V = \left\{ \frac{87}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{165x} +77 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & 594x-165x& = & 77+54 \\\Leftrightarrow & \color{red}{429} x& = & 131 \\\Leftrightarrow & x = \frac{131}{429} & & \\ & V = \left\{ \frac{131}{429} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-1)& = & 8x+\frac{5}{11} \\\Leftrightarrow & -21x+7& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{77}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+77} & = & \color{red}{88x} +5 \\\Leftrightarrow & -231x \color{red}{+77} \color{blue}{-77} \color{blue}{-88x} & = & \color{red}{88x} +5 \color{blue}{-88x} \color{blue}{-77} \\\Leftrightarrow & -231x-88x& = & 5-77 \\\Leftrightarrow & \color{red}{-319} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-319} & & \\\Leftrightarrow & x = \frac{72}{319} & & \\ & V = \left\{ \frac{72}{319} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 24x+\frac{18}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{50x} +45 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-36} \\\Leftrightarrow & 240x-50x& = & 45-36 \\\Leftrightarrow & \color{red}{190} x& = & 9 \\\Leftrightarrow & x = \frac{9}{190} & & \\ & V = \left\{ \frac{9}{190} \right\} & \\\end{align}\)