Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{9})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{25}{9}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+175} & = & \color{red}{189x} +27 \\\Leftrightarrow & 1260x \color{red}{+175} \color{blue}{-175} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{-175} \\\Leftrightarrow & 1260x-189x& = & 27-175 \\\Leftrightarrow & \color{red}{1071} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{1071} & & \\ & V = \left\{ \frac{-148}{1071} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{63x} +28 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-48} \\\Leftrightarrow & 336x-63x& = & 28-48 \\\Leftrightarrow & \color{red}{273} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{273} & & \\ & V = \left\{ \frac{-20}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+24} & = & \color{red}{-30x} +45 \\\Leftrightarrow & -180x \color{red}{+24} \color{blue}{-24} \color{blue}{+30x} & = & \color{red}{-30x} +45 \color{blue}{+30x} \color{blue}{-24} \\\Leftrightarrow & -180x+30x& = & 45-24 \\\Leftrightarrow & \color{red}{-150} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-150} & & \\\Leftrightarrow & x = \frac{-7}{50} & & \\ & V = \left\{ \frac{-7}{50} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{9})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -25x-\frac{25}{9}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{-175} & = & \color{red}{567x} +90 \\\Leftrightarrow & -1575x \color{red}{-175} \color{blue}{+175} \color{blue}{-567x} & = & \color{red}{567x} +90 \color{blue}{-567x} \color{blue}{+175} \\\Leftrightarrow & -1575x-567x& = & 90+175 \\\Leftrightarrow & \color{red}{-2142} x& = & 265 \\\Leftrightarrow & x = \frac{265}{-2142} & & \\\Leftrightarrow & x = \frac{-265}{2142} & & \\ & V = \left\{ \frac{-265}{2142} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{4}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+28} & = & \color{red}{-189x} +90 \\\Leftrightarrow & 504x \color{red}{+28} \color{blue}{-28} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{-28} \\\Leftrightarrow & 504x+189x& = & 90-28 \\\Leftrightarrow & \color{red}{693} x& = & 62 \\\Leftrightarrow & x = \frac{62}{693} & & \\ & V = \left\{ \frac{62}{693} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+4} \\\Leftrightarrow & 54x+63x& = & 6+4 \\\Leftrightarrow & \color{red}{117} x& = & 10 \\\Leftrightarrow & x = \frac{10}{117} & & \\ & V = \left\{ \frac{10}{117} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -8x+\frac{9}{10} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{-240x} +27 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{+240x} & = & \color{red}{-240x} +27 \color{blue}{+240x} \color{blue}{+140} \\\Leftrightarrow & 630x+240x& = & 27+140 \\\Leftrightarrow & \color{red}{870} x& = & 167 \\\Leftrightarrow & x = \frac{167}{870} & & \\ & V = \left\{ \frac{167}{870} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-70x} +9 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 90x+70x& = & 9-24 \\\Leftrightarrow & \color{red}{160} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{160} & & \\\Leftrightarrow & x = \frac{-3}{32} & & \\ & V = \left\{ \frac{-3}{32} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{5})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -14x-\frac{14}{5}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{-98} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -490x \color{red}{-98} \color{blue}{+98} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+98} \\\Leftrightarrow & -490x+105x& = & 50+98 \\\Leftrightarrow & \color{red}{-385} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-385} & & \\\Leftrightarrow & x = \frac{-148}{385} & & \\ & V = \left\{ \frac{-148}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{49x} +10 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & -210x-49x& = & 10-30 \\\Leftrightarrow & \color{red}{-259} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-259} & & \\\Leftrightarrow & x = \frac{20}{259} & & \\ & V = \left\{ \frac{20}{259} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{11})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x- \frac{70}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{-70} & = & \color{red}{198x} +33 \\\Leftrightarrow & 616x \color{red}{-70} \color{blue}{+70} \color{blue}{-198x} & = & \color{red}{198x} +33 \color{blue}{-198x} \color{blue}{+70} \\\Leftrightarrow & 616x-198x& = & 33+70 \\\Leftrightarrow & \color{red}{418} x& = & 103 \\\Leftrightarrow & x = \frac{103}{418} & & \\ & V = \left\{ \frac{103}{418} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{-135x} +12 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{+135x} & = & \color{red}{-135x} +12 \color{blue}{+135x} \color{blue}{+70} \\\Leftrightarrow & 420x+135x& = & 12+70 \\\Leftrightarrow & \color{red}{555} x& = & 82 \\\Leftrightarrow & x = \frac{82}{555} & & \\ & V = \left\{ \frac{82}{555} \right\} & \\\end{align}\)