Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+132} & = & \color{red}{165x} +20 \\\Leftrightarrow & 440x \color{red}{+132} \color{blue}{-132} \color{blue}{-165x} & = & \color{red}{165x} +20 \color{blue}{-165x} \color{blue}{-132} \\\Leftrightarrow & 440x-165x& = & 20-132 \\\Leftrightarrow & \color{red}{275} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{275} & & \\ & V = \left\{ \frac{-112}{275} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{10}{3}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{+10} & = & \color{red}{-24x} +4 \\\Leftrightarrow & -45x \color{red}{+10} \color{blue}{-10} \color{blue}{+24x} & = & \color{red}{-24x} +4 \color{blue}{+24x} \color{blue}{-10} \\\Leftrightarrow & -45x+24x& = & 4-10 \\\Leftrightarrow & \color{red}{-21} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-21} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{20}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-100} & = & \color{red}{105x} +6 \\\Leftrightarrow & 180x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 180x-105x& = & 6+100 \\\Leftrightarrow & \color{red}{75} x& = & 106 \\\Leftrightarrow & x = \frac{106}{75} & & \\ & V = \left\{ \frac{106}{75} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{105} x& = & 86 \\\Leftrightarrow & x = \frac{86}{105} & & \\ & V = \left\{ \frac{86}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{-55x} +9 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +9 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & -132x+55x& = & 9+18 \\\Leftrightarrow & \color{red}{-77} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-77} & & \\\Leftrightarrow & x = \frac{-27}{77} & & \\ & V = \left\{ \frac{-27}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+140} & = & \color{red}{105x} +24 \\\Leftrightarrow & 252x \color{red}{+140} \color{blue}{-140} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-140} \\\Leftrightarrow & 252x-105x& = & 24-140 \\\Leftrightarrow & \color{red}{147} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{147} & & \\ & V = \left\{ \frac{-116}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -16x+\frac{16}{9}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+16} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -144x \color{red}{+16} \color{blue}{-16} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-16} \\\Leftrightarrow & -144x+63x& = & 2-16 \\\Leftrightarrow & \color{red}{-81} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-81} & & \\\Leftrightarrow & x = \frac{14}{81} & & \\ & V = \left\{ \frac{14}{81} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{4})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 35x-\frac{35}{4}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{-315} & = & \color{red}{-108x} +16 \\\Leftrightarrow & 1260x \color{red}{-315} \color{blue}{+315} \color{blue}{+108x} & = & \color{red}{-108x} +16 \color{blue}{+108x} \color{blue}{+315} \\\Leftrightarrow & 1260x+108x& = & 16+315 \\\Leftrightarrow & \color{red}{1368} x& = & 331 \\\Leftrightarrow & x = \frac{331}{1368} & & \\ & V = \left\{ \frac{331}{1368} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+50} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 350x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & 350x+105x& = & 56-50 \\\Leftrightarrow & \color{red}{455} x& = & 6 \\\Leftrightarrow & x = \frac{6}{455} & & \\ & V = \left\{ \frac{6}{455} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{9})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 15x+\frac{10}{9}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{+110} & = & \color{red}{-693x} +81 \\\Leftrightarrow & 1485x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +81 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & 1485x+693x& = & 81-110 \\\Leftrightarrow & \color{red}{2178} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{2178} & & \\ & V = \left\{ \frac{-29}{2178} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{2})& = & 8x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{15}{2}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+165} & = & \color{red}{176x} +8 \\\Leftrightarrow & -330x \color{red}{+165} \color{blue}{-165} \color{blue}{-176x} & = & \color{red}{176x} +8 \color{blue}{-176x} \color{blue}{-165} \\\Leftrightarrow & -330x-176x& = & 8-165 \\\Leftrightarrow & \color{red}{-506} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-506} & & \\\Leftrightarrow & x = \frac{157}{506} & & \\ & V = \left\{ \frac{157}{506} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 6x-\frac{10}{3}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{144}{ \color{blue}{24} }x- \frac{80}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 144x \color{red}{-80} & = & \color{red}{-168x} +9 \\\Leftrightarrow & 144x \color{red}{-80} \color{blue}{+80} \color{blue}{+168x} & = & \color{red}{-168x} +9 \color{blue}{+168x} \color{blue}{+80} \\\Leftrightarrow & 144x+168x& = & 9+80 \\\Leftrightarrow & \color{red}{312} x& = & 89 \\\Leftrightarrow & x = \frac{89}{312} & & \\ & V = \left\{ \frac{89}{312} \right\} & \\\end{align}\)