Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{5})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -6x-\frac{8}{5}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{32}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-32} & = & \color{red}{-140x} +45 \\\Leftrightarrow & -120x \color{red}{-32} \color{blue}{+32} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{+32} \\\Leftrightarrow & -120x+140x& = & 45+32 \\\Leftrightarrow & \color{red}{20} x& = & 77 \\\Leftrightarrow & x = \frac{77}{20} & & \\ & V = \left\{ \frac{77}{20} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -4x+\frac{4}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+12} & = & \color{red}{165x} +77 \\\Leftrightarrow & -132x \color{red}{+12} \color{blue}{-12} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{-12} \\\Leftrightarrow & -132x-165x& = & 77-12 \\\Leftrightarrow & \color{red}{-297} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-297} & & \\\Leftrightarrow & x = \frac{-65}{297} & & \\ & V = \left\{ \frac{-65}{297} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-140} & = & \color{red}{96x} +9 \\\Leftrightarrow & -252x \color{red}{-140} \color{blue}{+140} \color{blue}{-96x} & = & \color{red}{96x} +9 \color{blue}{-96x} \color{blue}{+140} \\\Leftrightarrow & -252x-96x& = & 9+140 \\\Leftrightarrow & \color{red}{-348} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-348} & & \\\Leftrightarrow & x = \frac{-149}{348} & & \\ & V = \left\{ \frac{-149}{348} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -16x+\frac{8}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+88} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -1232x \color{red}{+88} \color{blue}{-88} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-88} \\\Leftrightarrow & -1232x+539x& = & 28-88 \\\Leftrightarrow & \color{red}{-693} x& = & -60 \\\Leftrightarrow & x = \frac{-60}{-693} & & \\\Leftrightarrow & x = \frac{20}{231} & & \\ & V = \left\{ \frac{20}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{3})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 6x+\frac{4}{3}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{30x} +15 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{-30x} & = & \color{red}{30x} +15 \color{blue}{-30x} \color{blue}{-8} \\\Leftrightarrow & 36x-30x& = & 15-8 \\\Leftrightarrow & \color{red}{6} x& = & 7 \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{8})& = & -6x+\frac{3}{10} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -6x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-240}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{-240x} +12 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+240x} & = & \color{red}{-240x} +12 \color{blue}{+240x} \color{blue}{-105} \\\Leftrightarrow & -1400x+240x& = & 12-105 \\\Leftrightarrow & \color{red}{-1160} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-1160} & & \\\Leftrightarrow & x = \frac{93}{1160} & & \\ & V = \left\{ \frac{93}{1160} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{70x} +63 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & 84x-70x& = & 63-12 \\\Leftrightarrow & \color{red}{14} x& = & 51 \\\Leftrightarrow & x = \frac{51}{14} & & \\ & V = \left\{ \frac{51}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 180x+75x& = & 50+36 \\\Leftrightarrow & \color{red}{255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{255} & & \\ & V = \left\{ \frac{86}{255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+154} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -462x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & -462x+99x& = & 6-154 \\\Leftrightarrow & \color{red}{-363} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-363} & & \\\Leftrightarrow & x = \frac{148}{363} & & \\ & V = \left\{ \frac{148}{363} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{20}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+100} & = & \color{red}{245x} +42 \\\Leftrightarrow & -350x \color{red}{+100} \color{blue}{-100} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-100} \\\Leftrightarrow & -350x-245x& = & 42-100 \\\Leftrightarrow & \color{red}{-595} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-595} & & \\\Leftrightarrow & x = \frac{58}{595} & & \\ & V = \left\{ \frac{58}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{4}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+36} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 594x \color{red}{+36} \color{blue}{-36} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-36} \\\Leftrightarrow & 594x+495x& = & 88-36 \\\Leftrightarrow & \color{red}{1089} x& = & 52 \\\Leftrightarrow & x = \frac{52}{1089} & & \\ & V = \left\{ \frac{52}{1089} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 28x+\frac{14}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{+154} & = & \color{red}{275x} +30 \\\Leftrightarrow & 1540x \color{red}{+154} \color{blue}{-154} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-154} \\\Leftrightarrow & 1540x-275x& = & 30-154 \\\Leftrightarrow & \color{red}{1265} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{1265} & & \\ & V = \left\{ \frac{-124}{1265} \right\} & \\\end{align}\)