Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{175x} +50 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 420x-175x& = & 50-84 \\\Leftrightarrow & \color{red}{245} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{245} & & \\ & V = \left\{ \frac{-34}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+6} & = & \color{red}{35x} +6 \\\Leftrightarrow & 84x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 84x-35x& = & 6-6 \\\Leftrightarrow & \color{red}{49} x& = & 0 \\\Leftrightarrow & x = \frac{0}{49} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{-595} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-595} & & \\\Leftrightarrow & x = \frac{108}{595} & & \\ & V = \left\{ \frac{108}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{2})& = & 4x+\frac{5}{7} \\\Leftrightarrow & -28x+\frac{21}{2}& = & 4x+\frac{5}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-392}{ \color{blue}{14} }x+ \frac{147}{ \color{blue}{14} })& = & (\frac{56}{ \color{blue}{14} }x+ \frac{10}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -392x \color{red}{+147} & = & \color{red}{56x} +10 \\\Leftrightarrow & -392x \color{red}{+147} \color{blue}{-147} \color{blue}{-56x} & = & \color{red}{56x} +10 \color{blue}{-56x} \color{blue}{-147} \\\Leftrightarrow & -392x-56x& = & 10-147 \\\Leftrightarrow & \color{red}{-448} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-448} & & \\\Leftrightarrow & x = \frac{137}{448} & & \\ & V = \left\{ \frac{137}{448} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{16}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-48} & = & \color{red}{165x} +110 \\\Leftrightarrow & 396x \color{red}{-48} \color{blue}{+48} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+48} \\\Leftrightarrow & 396x-165x& = & 110+48 \\\Leftrightarrow & \color{red}{231} x& = & 158 \\\Leftrightarrow & x = \frac{158}{231} & & \\ & V = \left\{ \frac{158}{231} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{14}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{42}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-42} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 924x \color{red}{-42} \color{blue}{+42} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+42} \\\Leftrightarrow & 924x+165x& = & 22+42 \\\Leftrightarrow & \color{red}{1089} x& = & 64 \\\Leftrightarrow & x = \frac{64}{1089} & & \\ & V = \left\{ \frac{64}{1089} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+30} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -350x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -350x+245x& = & 14-30 \\\Leftrightarrow & \color{red}{-105} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-105} & & \\\Leftrightarrow & x = \frac{16}{105} & & \\ & V = \left\{ \frac{16}{105} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{245x} +20 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 420x-245x& = & 20+84 \\\Leftrightarrow & \color{red}{175} x& = & 104 \\\Leftrightarrow & x = \frac{104}{175} & & \\ & V = \left\{ \frac{104}{175} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+90} & = & \color{red}{165x} +77 \\\Leftrightarrow & -396x \color{red}{+90} \color{blue}{-90} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{-90} \\\Leftrightarrow & -396x-165x& = & 77-90 \\\Leftrightarrow & \color{red}{-561} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-561} & & \\\Leftrightarrow & x = \frac{13}{561} & & \\ & V = \left\{ \frac{13}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+18} & = & \color{red}{55x} +5 \\\Leftrightarrow & 198x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 198x-55x& = & 5-18 \\\Leftrightarrow & \color{red}{143} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{143} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{9})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{20}{9}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-220} & = & \color{red}{495x} +54 \\\Leftrightarrow & 1188x \color{red}{-220} \color{blue}{+220} \color{blue}{-495x} & = & \color{red}{495x} +54 \color{blue}{-495x} \color{blue}{+220} \\\Leftrightarrow & 1188x-495x& = & 54+220 \\\Leftrightarrow & \color{red}{693} x& = & 274 \\\Leftrightarrow & x = \frac{274}{693} & & \\ & V = \left\{ \frac{274}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{9})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{20}{9}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+20} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -108x \color{red}{+20} \color{blue}{-20} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-20} \\\Leftrightarrow & -108x+45x& = & 6-20 \\\Leftrightarrow & \color{red}{-63} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-63} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)