Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{12}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-132} & = & \color{red}{539x} +56 \\\Leftrightarrow & 616x \color{red}{-132} \color{blue}{+132} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{+132} \\\Leftrightarrow & 616x-539x& = & 56+132 \\\Leftrightarrow & \color{red}{77} x& = & 188 \\\Leftrightarrow & x = \frac{188}{77} & & \\ & V = \left\{ \frac{188}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{3})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 8x+\frac{16}{3}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+48} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 72x \color{red}{+48} \color{blue}{-48} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-48} \\\Leftrightarrow & 72x+27x& = & 8-48 \\\Leftrightarrow & \color{red}{99} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{99} & & \\ & V = \left\{ \frac{-40}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{-90} \\\Leftrightarrow & 594x+165x& = & 110-90 \\\Leftrightarrow & \color{red}{759} x& = & 20 \\\Leftrightarrow & x = \frac{20}{759} & & \\ & V = \left\{ \frac{20}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & -9x+\frac{5}{9} \\\Leftrightarrow & 20x-\frac{10}{3}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-30} & = & \color{red}{-81x} +5 \\\Leftrightarrow & 180x \color{red}{-30} \color{blue}{+30} \color{blue}{+81x} & = & \color{red}{-81x} +5 \color{blue}{+81x} \color{blue}{+30} \\\Leftrightarrow & 180x+81x& = & 5+30 \\\Leftrightarrow & \color{red}{261} x& = & 35 \\\Leftrightarrow & x = \frac{35}{261} & & \\ & V = \left\{ \frac{35}{261} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-18} & = & \color{red}{-55x} +2 \\\Leftrightarrow & 132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 132x+55x& = & 2+18 \\\Leftrightarrow & \color{red}{187} x& = & 20 \\\Leftrightarrow & x = \frac{20}{187} & & \\ & V = \left\{ \frac{20}{187} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+54} & = & \color{red}{-567x} +14 \\\Leftrightarrow & 630x \color{red}{+54} \color{blue}{-54} \color{blue}{+567x} & = & \color{red}{-567x} +14 \color{blue}{+567x} \color{blue}{-54} \\\Leftrightarrow & 630x+567x& = & 14-54 \\\Leftrightarrow & \color{red}{1197} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{1197} & & \\ & V = \left\{ \frac{-40}{1197} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+63} & = & \color{red}{192x} +80 \\\Leftrightarrow & -504x \color{red}{+63} \color{blue}{-63} \color{blue}{-192x} & = & \color{red}{192x} +80 \color{blue}{-192x} \color{blue}{-63} \\\Leftrightarrow & -504x-192x& = & 80-63 \\\Leftrightarrow & \color{red}{-696} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-696} & & \\\Leftrightarrow & x = \frac{-17}{696} & & \\ & V = \left\{ \frac{-17}{696} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+18} & = & \color{red}{55x} +5 \\\Leftrightarrow & 264x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 264x-55x& = & 5-18 \\\Leftrightarrow & \color{red}{209} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{209} & & \\ & V = \left\{ \frac{-13}{209} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+12} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -84x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & -84x+98x& = & 63-12 \\\Leftrightarrow & \color{red}{14} x& = & 51 \\\Leftrightarrow & x = \frac{51}{14} & & \\ & V = \left\{ \frac{51}{14} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{7})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{25}{7}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{275}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+275} & = & \color{red}{-231x} +14 \\\Leftrightarrow & 770x \color{red}{+275} \color{blue}{-275} \color{blue}{+231x} & = & \color{red}{-231x} +14 \color{blue}{+231x} \color{blue}{-275} \\\Leftrightarrow & 770x+231x& = & 14-275 \\\Leftrightarrow & \color{red}{1001} x& = & -261 \\\Leftrightarrow & x = \frac{-261}{1001} & & \\ & V = \left\{ \frac{-261}{1001} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+10} & = & \color{red}{-28x} +8 \\\Leftrightarrow & -105x \color{red}{+10} \color{blue}{-10} \color{blue}{+28x} & = & \color{red}{-28x} +8 \color{blue}{+28x} \color{blue}{-10} \\\Leftrightarrow & -105x+28x& = & 8-10 \\\Leftrightarrow & \color{red}{-77} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-77} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+216} & = & \color{red}{-225x} +50 \\\Leftrightarrow & -540x \color{red}{+216} \color{blue}{-216} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-216} \\\Leftrightarrow & -540x+225x& = & 50-216 \\\Leftrightarrow & \color{red}{-315} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-315} & & \\\Leftrightarrow & x = \frac{166}{315} & & \\ & V = \left\{ \frac{166}{315} \right\} & \\\end{align}\)