Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+8} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-8} \\\Leftrightarrow & 24x+15x& = & 8-8 \\\Leftrightarrow & \color{red}{39} x& = & 0 \\\Leftrightarrow & x = \frac{0}{39} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+54} & = & \color{red}{165x} +110 \\\Leftrightarrow & 594x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & 594x-165x& = & 110-54 \\\Leftrightarrow & \color{red}{429} x& = & 56 \\\Leftrightarrow & x = \frac{56}{429} & & \\ & V = \left\{ \frac{56}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{3})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{10}{3}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{-20} & = & \color{red}{-54x} +15 \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{+20} \\\Leftrightarrow & -24x+54x& = & 15+20 \\\Leftrightarrow & \color{red}{30} x& = & 35 \\\Leftrightarrow & x = \frac{35}{30} & & \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{8}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{135x} +10 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{-24} \\\Leftrightarrow & 120x-135x& = & 10-24 \\\Leftrightarrow & \color{red}{-15} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-15} & & \\\Leftrightarrow & x = \frac{14}{15} & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -120x+25x& = & 8-12 \\\Leftrightarrow & \color{red}{-95} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-95} & & \\\Leftrightarrow & x = \frac{4}{95} & & \\ & V = \left\{ \frac{4}{95} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{9}{5} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{275x} +99 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{-275x} & = & \color{red}{275x} +99 \color{blue}{-275x} \color{blue}{+60} \\\Leftrightarrow & -660x-275x& = & 99+60 \\\Leftrightarrow & \color{red}{-935} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-935} & & \\\Leftrightarrow & x = \frac{-159}{935} & & \\ & V = \left\{ \frac{-159}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+12} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -112x \color{red}{+12} \color{blue}{-12} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-12} \\\Leftrightarrow & -112x+126x& = & 21-12 \\\Leftrightarrow & \color{red}{14} x& = & 9 \\\Leftrightarrow & x = \frac{9}{14} & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+72} \\\Leftrightarrow & 270x+75x& = & 50+72 \\\Leftrightarrow & \color{red}{345} x& = & 122 \\\Leftrightarrow & x = \frac{122}{345} & & \\ & V = \left\{ \frac{122}{345} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{135x} +24 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & 120x-135x& = & 24+40 \\\Leftrightarrow & \color{red}{-15} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-15} & & \\\Leftrightarrow & x = \frac{-64}{15} & & \\ & V = \left\{ \frac{-64}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+8} & = & \color{red}{45x} +5 \\\Leftrightarrow & 54x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +5 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 54x-45x& = & 5-8 \\\Leftrightarrow & \color{red}{9} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{9} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-168}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -168x \color{red}{-36} & = & \color{red}{210x} +35 \\\Leftrightarrow & -168x \color{red}{-36} \color{blue}{+36} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+36} \\\Leftrightarrow & -168x-210x& = & 35+36 \\\Leftrightarrow & \color{red}{-378} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-378} & & \\\Leftrightarrow & x = \frac{-71}{378} & & \\ & V = \left\{ \frac{-71}{378} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-132} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -825x \color{red}{-132} \color{blue}{+132} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{+132} \\\Leftrightarrow & -825x+220x& = & 30+132 \\\Leftrightarrow & \color{red}{-605} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-605} & & \\\Leftrightarrow & x = \frac{-162}{605} & & \\ & V = \left\{ \frac{-162}{605} \right\} & \\\end{align}\)