Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-54} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 990x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & 990x+231x& = & 88+54 \\\Leftrightarrow & \color{red}{1221} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1221} & & \\ & V = \left\{ \frac{142}{1221} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{4})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{35}{4}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{420}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{160x} +24 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-160x} & = & \color{red}{160x} +24 \color{blue}{-160x} \color{blue}{+175} \\\Leftrightarrow & 420x-160x& = & 24+175 \\\Leftrightarrow & \color{red}{260} x& = & 199 \\\Leftrightarrow & x = \frac{199}{260} & & \\ & V = \left\{ \frac{199}{260} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{20}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+60} & = & \color{red}{231x} +22 \\\Leftrightarrow & -528x \color{red}{+60} \color{blue}{-60} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-60} \\\Leftrightarrow & -528x-231x& = & 22-60 \\\Leftrightarrow & \color{red}{-759} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-759} & & \\\Leftrightarrow & x = \frac{38}{759} & & \\ & V = \left\{ \frac{38}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{75x} +20 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{-12} \\\Leftrightarrow & -60x-75x& = & 20-12 \\\Leftrightarrow & \color{red}{-135} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-135} & & \\\Leftrightarrow & x = \frac{-8}{135} & & \\ & V = \left\{ \frac{-8}{135} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{315x} +30 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{-315x} & = & \color{red}{315x} +30 \color{blue}{-315x} \color{blue}{+28} \\\Leftrightarrow & 140x-315x& = & 30+28 \\\Leftrightarrow & \color{red}{-175} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-175} & & \\\Leftrightarrow & x = \frac{-58}{175} & & \\ & V = \left\{ \frac{-58}{175} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{42x} +9 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & 120x-42x& = & 9+40 \\\Leftrightarrow & \color{red}{78} x& = & 49 \\\Leftrightarrow & x = \frac{49}{78} & & \\ & V = \left\{ \frac{49}{78} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{9}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{81}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-81} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -756x \color{red}{-81} \color{blue}{+81} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+81} \\\Leftrightarrow & -756x+315x& = & 56+81 \\\Leftrightarrow & \color{red}{-441} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-441} & & \\\Leftrightarrow & x = \frac{-137}{441} & & \\ & V = \left\{ \frac{-137}{441} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -25x+\frac{20}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{+20} & = & \color{red}{15x} +10 \\\Leftrightarrow & -75x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & -75x-15x& = & 10-20 \\\Leftrightarrow & \color{red}{-90} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-90} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{-14} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -140x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & -140x+15x& = & 4+14 \\\Leftrightarrow & \color{red}{-125} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-125} & & \\\Leftrightarrow & x = \frac{-18}{125} & & \\ & V = \left\{ \frac{-18}{125} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{8}{9}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-40} & = & \color{red}{225x} +18 \\\Leftrightarrow & -540x \color{red}{-40} \color{blue}{+40} \color{blue}{-225x} & = & \color{red}{225x} +18 \color{blue}{-225x} \color{blue}{+40} \\\Leftrightarrow & -540x-225x& = & 18+40 \\\Leftrightarrow & \color{red}{-765} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-765} & & \\\Leftrightarrow & x = \frac{-58}{765} & & \\ & V = \left\{ \frac{-58}{765} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{-81x} +15 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +15 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & -72x+81x& = & 15-8 \\\Leftrightarrow & \color{red}{9} x& = & 7 \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & 9x+\frac{8}{11} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+110} & = & \color{red}{693x} +56 \\\Leftrightarrow & 616x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +56 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & 616x-693x& = & 56-110 \\\Leftrightarrow & \color{red}{-77} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-77} & & \\\Leftrightarrow & x = \frac{54}{77} & & \\ & V = \left\{ \frac{54}{77} \right\} & \\\end{align}\)