Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-132} & = & \color{red}{275x} +30 \\\Leftrightarrow & 330x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 330x-275x& = & 30+132 \\\Leftrightarrow & \color{red}{55} x& = & 162 \\\Leftrightarrow & x = \frac{162}{55} & & \\ & V = \left\{ \frac{162}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -462x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -462x+539x& = & 42+110 \\\Leftrightarrow & \color{red}{77} x& = & 152 \\\Leftrightarrow & x = \frac{152}{77} & & \\ & V = \left\{ \frac{152}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-110} & = & \color{red}{385x} +21 \\\Leftrightarrow & 462x \color{red}{-110} \color{blue}{+110} \color{blue}{-385x} & = & \color{red}{385x} +21 \color{blue}{-385x} \color{blue}{+110} \\\Leftrightarrow & 462x-385x& = & 21+110 \\\Leftrightarrow & \color{red}{77} x& = & 131 \\\Leftrightarrow & x = \frac{131}{77} & & \\ & V = \left\{ \frac{131}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{5})& = & 2x+\frac{9}{5} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 2x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{175}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 175x \color{red}{-14} & = & \color{red}{10x} +9 \\\Leftrightarrow & 175x \color{red}{-14} \color{blue}{+14} \color{blue}{-10x} & = & \color{red}{10x} +9 \color{blue}{-10x} \color{blue}{+14} \\\Leftrightarrow & 175x-10x& = & 9+14 \\\Leftrightarrow & \color{red}{165} x& = & 23 \\\Leftrightarrow & x = \frac{23}{165} & & \\ & V = \left\{ \frac{23}{165} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-99} & = & \color{red}{385x} +40 \\\Leftrightarrow & -495x \color{red}{-99} \color{blue}{+99} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+99} \\\Leftrightarrow & -495x-385x& = & 40+99 \\\Leftrightarrow & \color{red}{-880} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-880} & & \\\Leftrightarrow & x = \frac{-139}{880} & & \\ & V = \left\{ \frac{-139}{880} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & -9x+\frac{3}{11} \\\Leftrightarrow & 4x+\frac{8}{11}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{+8} & = & \color{red}{-99x} +3 \\\Leftrightarrow & 44x \color{red}{+8} \color{blue}{-8} \color{blue}{+99x} & = & \color{red}{-99x} +3 \color{blue}{+99x} \color{blue}{-8} \\\Leftrightarrow & 44x+99x& = & 3-8 \\\Leftrightarrow & \color{red}{143} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{143} & & \\ & V = \left\{ \frac{-5}{143} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+54} & = & \color{red}{75x} +10 \\\Leftrightarrow & 270x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & 270x-75x& = & 10-54 \\\Leftrightarrow & \color{red}{195} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{195} & & \\ & V = \left\{ \frac{-44}{195} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-100} & = & \color{red}{-105x} +6 \\\Leftrightarrow & 300x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & 300x+105x& = & 6+100 \\\Leftrightarrow & \color{red}{405} x& = & 106 \\\Leftrightarrow & x = \frac{106}{405} & & \\ & V = \left\{ \frac{106}{405} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{7}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{539x} +49 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +49 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1232x-539x& = & 49+176 \\\Leftrightarrow & \color{red}{-1771} x& = & 225 \\\Leftrightarrow & x = \frac{225}{-1771} & & \\\Leftrightarrow & x = \frac{-225}{1771} & & \\ & V = \left\{ \frac{-225}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{+144} & = & \color{red}{180x} +35 \\\Leftrightarrow & -1200x \color{red}{+144} \color{blue}{-144} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{-144} \\\Leftrightarrow & -1200x-180x& = & 35-144 \\\Leftrightarrow & \color{red}{-1380} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1380} & & \\\Leftrightarrow & x = \frac{109}{1380} & & \\ & V = \left\{ \frac{109}{1380} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{4})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{+135} & = & \color{red}{-108x} +32 \\\Leftrightarrow & 360x \color{red}{+135} \color{blue}{-135} \color{blue}{+108x} & = & \color{red}{-108x} +32 \color{blue}{+108x} \color{blue}{-135} \\\Leftrightarrow & 360x+108x& = & 32-135 \\\Leftrightarrow & \color{red}{468} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{468} & & \\ & V = \left\{ \frac{-103}{468} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 4x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{48x} +10 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{-48x} & = & \color{red}{48x} +10 \color{blue}{-48x} \color{blue}{-45} \\\Leftrightarrow & 180x-48x& = & 10-45 \\\Leftrightarrow & \color{red}{132} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{132} & & \\ & V = \left\{ \frac{-35}{132} \right\} & \\\end{align}\)