Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+6} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 84x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 84x+35x& = & 2-6 \\\Leftrightarrow & \color{red}{119} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{119} & & \\ & V = \left\{ \frac{-4}{119} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-4} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 30x \color{red}{-4} \color{blue}{+4} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+4} \\\Leftrightarrow & 30x+25x& = & 6+4 \\\Leftrightarrow & \color{red}{55} x& = & 10 \\\Leftrightarrow & x = \frac{10}{55} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -2x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-48x} +32 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +32 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & -672x+48x& = & 32-63 \\\Leftrightarrow & \color{red}{-624} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-624} & & \\\Leftrightarrow & x = \frac{31}{624} & & \\ & V = \left\{ \frac{31}{624} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & -4x+\frac{9}{10} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{-40x} +9 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{+48} \\\Leftrightarrow & -180x+40x& = & 9+48 \\\Leftrightarrow & \color{red}{-140} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-140} & & \\\Leftrightarrow & x = \frac{-57}{140} & & \\ & V = \left\{ \frac{-57}{140} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-30} & = & \color{red}{-35x} +5 \\\Leftrightarrow & 168x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +5 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & 168x+35x& = & 5+30 \\\Leftrightarrow & \color{red}{203} x& = & 35 \\\Leftrightarrow & x = \frac{35}{203} & & \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 16x+\frac{16}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{112}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+112} & = & \color{red}{-147x} +12 \\\Leftrightarrow & 336x \color{red}{+112} \color{blue}{-112} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{-112} \\\Leftrightarrow & 336x+147x& = & 12-112 \\\Leftrightarrow & \color{red}{483} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{483} & & \\ & V = \left\{ \frac{-100}{483} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{3})& = & 2x+\frac{7}{12} \\\Leftrightarrow & 21x+\frac{35}{3}& = & 2x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{+140} & = & \color{red}{24x} +7 \\\Leftrightarrow & 252x \color{red}{+140} \color{blue}{-140} \color{blue}{-24x} & = & \color{red}{24x} +7 \color{blue}{-24x} \color{blue}{-140} \\\Leftrightarrow & 252x-24x& = & 7-140 \\\Leftrightarrow & \color{red}{228} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{228} & & \\\Leftrightarrow & x = \frac{-7}{12} & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-216} & = & \color{red}{315x} +40 \\\Leftrightarrow & 1350x \color{red}{-216} \color{blue}{+216} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+216} \\\Leftrightarrow & 1350x-315x& = & 40+216 \\\Leftrightarrow & \color{red}{1035} x& = & 256 \\\Leftrightarrow & x = \frac{256}{1035} & & \\ & V = \left\{ \frac{256}{1035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{15}{8}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+45} & = & \color{red}{168x} +16 \\\Leftrightarrow & 240x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +16 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & 240x-168x& = & 16-45 \\\Leftrightarrow & \color{red}{72} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{72} & & \\ & V = \left\{ \frac{-29}{72} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{9})& = & 8x+\frac{7}{8} \\\Leftrightarrow & -15x+\frac{20}{9}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{160}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+160} & = & \color{red}{576x} +63 \\\Leftrightarrow & -1080x \color{red}{+160} \color{blue}{-160} \color{blue}{-576x} & = & \color{red}{576x} +63 \color{blue}{-576x} \color{blue}{-160} \\\Leftrightarrow & -1080x-576x& = & 63-160 \\\Leftrightarrow & \color{red}{-1656} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1656} & & \\\Leftrightarrow & x = \frac{97}{1656} & & \\ & V = \left\{ \frac{97}{1656} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-50} & = & \color{red}{-315x} +28 \\\Leftrightarrow & -700x \color{red}{-50} \color{blue}{+50} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{+50} \\\Leftrightarrow & -700x+315x& = & 28+50 \\\Leftrightarrow & \color{red}{-385} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-385} & & \\\Leftrightarrow & x = \frac{-78}{385} & & \\ & V = \left\{ \frac{-78}{385} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{7})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-110} & = & \color{red}{231x} +21 \\\Leftrightarrow & -616x \color{red}{-110} \color{blue}{+110} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{+110} \\\Leftrightarrow & -616x-231x& = & 21+110 \\\Leftrightarrow & \color{red}{-847} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-847} & & \\\Leftrightarrow & x = \frac{-131}{847} & & \\ & V = \left\{ \frac{-131}{847} \right\} & \\\end{align}\)