Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-264} & = & \color{red}{275x} +25 \\\Leftrightarrow & 660x \color{red}{-264} \color{blue}{+264} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+264} \\\Leftrightarrow & 660x-275x& = & 25+264 \\\Leftrightarrow & \color{red}{385} x& = & 289 \\\Leftrightarrow & x = \frac{289}{385} & & \\ & V = \left\{ \frac{289}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+40} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -60x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & -60x+42x& = & 5-40 \\\Leftrightarrow & \color{red}{-18} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-18} & & \\\Leftrightarrow & x = \frac{35}{18} & & \\ & V = \left\{ \frac{35}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-60} & = & \color{red}{-168x} +14 \\\Leftrightarrow & 525x \color{red}{-60} \color{blue}{+60} \color{blue}{+168x} & = & \color{red}{-168x} +14 \color{blue}{+168x} \color{blue}{+60} \\\Leftrightarrow & 525x+168x& = & 14+60 \\\Leftrightarrow & \color{red}{693} x& = & 74 \\\Leftrightarrow & x = \frac{74}{693} & & \\ & V = \left\{ \frac{74}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{11})& = & -6x+\frac{7}{2} \\\Leftrightarrow & -35x+\frac{14}{11}& = & -6x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-770}{ \color{blue}{22} }x+ \frac{28}{ \color{blue}{22} })& = & (\frac{-132}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -770x \color{red}{+28} & = & \color{red}{-132x} +77 \\\Leftrightarrow & -770x \color{red}{+28} \color{blue}{-28} \color{blue}{+132x} & = & \color{red}{-132x} +77 \color{blue}{+132x} \color{blue}{-28} \\\Leftrightarrow & -770x+132x& = & 77-28 \\\Leftrightarrow & \color{red}{-638} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-638} & & \\\Leftrightarrow & x = \frac{-49}{638} & & \\ & V = \left\{ \frac{-49}{638} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+84} & = & \color{red}{175x} +45 \\\Leftrightarrow & -840x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -840x-175x& = & 45-84 \\\Leftrightarrow & \color{red}{-1015} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-1015} & & \\\Leftrightarrow & x = \frac{39}{1015} & & \\ & V = \left\{ \frac{39}{1015} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{15}{2}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+105} & = & \color{red}{98x} +4 \\\Leftrightarrow & -140x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +4 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & -140x-98x& = & 4-105 \\\Leftrightarrow & \color{red}{-238} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{-238} & & \\\Leftrightarrow & x = \frac{101}{238} & & \\ & V = \left\{ \frac{101}{238} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{11})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 15x-\frac{25}{11}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-125} & = & \color{red}{385x} +99 \\\Leftrightarrow & 825x \color{red}{-125} \color{blue}{+125} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+125} \\\Leftrightarrow & 825x-385x& = & 99+125 \\\Leftrightarrow & \color{red}{440} x& = & 224 \\\Leftrightarrow & x = \frac{224}{440} & & \\\Leftrightarrow & x = \frac{28}{55} & & \\ & V = \left\{ \frac{28}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{5})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 28x-\frac{14}{5}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1120}{ \color{blue}{40} }x- \frac{112}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1120x \color{red}{-112} & = & \color{red}{-120x} +35 \\\Leftrightarrow & 1120x \color{red}{-112} \color{blue}{+112} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{+112} \\\Leftrightarrow & 1120x+120x& = & 35+112 \\\Leftrightarrow & \color{red}{1240} x& = & 147 \\\Leftrightarrow & x = \frac{147}{1240} & & \\ & V = \left\{ \frac{147}{1240} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+42} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -525x \color{red}{+42} \color{blue}{-42} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-42} \\\Leftrightarrow & -525x+135x& = & 40-42 \\\Leftrightarrow & \color{red}{-390} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-390} & & \\\Leftrightarrow & x = \frac{1}{195} & & \\ & V = \left\{ \frac{1}{195} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{275x} +66 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-120} \\\Leftrightarrow & 1320x-275x& = & 66-120 \\\Leftrightarrow & \color{red}{1045} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{1045} & & \\ & V = \left\{ \frac{-54}{1045} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+50} & = & \color{red}{315x} +42 \\\Leftrightarrow & -280x \color{red}{+50} \color{blue}{-50} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{-50} \\\Leftrightarrow & -280x-315x& = & 42-50 \\\Leftrightarrow & \color{red}{-595} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-595} & & \\\Leftrightarrow & x = \frac{8}{595} & & \\ & V = \left\{ \frac{8}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{35x} +9 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & 84x-35x& = & 9+30 \\\Leftrightarrow & \color{red}{49} x& = & 39 \\\Leftrightarrow & x = \frac{39}{49} & & \\ & V = \left\{ \frac{39}{49} \right\} & \\\end{align}\)