Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 15x+\frac{15}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{60}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{196x} +35 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-60} \\\Leftrightarrow & 420x-196x& = & 35-60 \\\Leftrightarrow & \color{red}{224} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{224} & & \\ & V = \left\{ \frac{-25}{224} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & 4x+\frac{8}{7} \\\Leftrightarrow & 9x+\frac{15}{4}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{112}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{112x} +32 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{-112x} & = & \color{red}{112x} +32 \color{blue}{-112x} \color{blue}{-105} \\\Leftrightarrow & 252x-112x& = & 32-105 \\\Leftrightarrow & \color{red}{140} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{140} & & \\ & V = \left\{ \frac{-73}{140} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-16} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -56x \color{red}{-16} \color{blue}{+16} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+16} \\\Leftrightarrow & -56x+63x& = & 4+16 \\\Leftrightarrow & \color{red}{7} x& = & 20 \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 12x+\frac{24}{11}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{792}{ \color{blue}{66} }x+ \frac{144}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 792x \color{red}{+144} & = & \color{red}{330x} +77 \\\Leftrightarrow & 792x \color{red}{+144} \color{blue}{-144} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{-144} \\\Leftrightarrow & 792x-330x& = & 77-144 \\\Leftrightarrow & \color{red}{462} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{462} & & \\ & V = \left\{ \frac{-67}{462} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{7}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{-275x} +35 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +35 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -660x+275x& = & 35-132 \\\Leftrightarrow & \color{red}{-385} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-385} & & \\\Leftrightarrow & x = \frac{97}{385} & & \\ & V = \left\{ \frac{97}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 4x+\frac{6}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+18} & = & \color{red}{45x} +40 \\\Leftrightarrow & 60x \color{red}{+18} \color{blue}{-18} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{-18} \\\Leftrightarrow & 60x-45x& = & 40-18 \\\Leftrightarrow & \color{red}{15} x& = & 22 \\\Leftrightarrow & x = \frac{22}{15} & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 4x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{176x} +20 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{-176x} & = & \color{red}{176x} +20 \color{blue}{-176x} \color{blue}{+165} \\\Leftrightarrow & -660x-176x& = & 20+165 \\\Leftrightarrow & \color{red}{-836} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-836} & & \\\Leftrightarrow & x = \frac{-185}{836} & & \\ & V = \left\{ \frac{-185}{836} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-48} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{-48} \color{blue}{+48} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+48} \\\Leftrightarrow & 252x-105x& = & 56+48 \\\Leftrightarrow & \color{red}{147} x& = & 104 \\\Leftrightarrow & x = \frac{104}{147} & & \\ & V = \left\{ \frac{104}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+270} & = & \color{red}{-315x} +28 \\\Leftrightarrow & 756x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & 756x+315x& = & 28-270 \\\Leftrightarrow & \color{red}{1071} x& = & -242 \\\Leftrightarrow & x = \frac{-242}{1071} & & \\ & V = \left\{ \frac{-242}{1071} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+56} & = & \color{red}{441x} +81 \\\Leftrightarrow & -630x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +81 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -630x-441x& = & 81-56 \\\Leftrightarrow & \color{red}{-1071} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-1071} & & \\\Leftrightarrow & x = \frac{-25}{1071} & & \\ & V = \left\{ \frac{-25}{1071} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+72} & = & \color{red}{200x} +15 \\\Leftrightarrow & 480x \color{red}{+72} \color{blue}{-72} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{-72} \\\Leftrightarrow & 480x-200x& = & 15-72 \\\Leftrightarrow & \color{red}{280} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{280} & & \\ & V = \left\{ \frac{-57}{280} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{7})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x+\frac{20}{7}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{105x} +49 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{-105x} & = & \color{red}{105x} +49 \color{blue}{-105x} \color{blue}{-60} \\\Leftrightarrow & -252x-105x& = & 49-60 \\\Leftrightarrow & \color{red}{-357} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-357} & & \\\Leftrightarrow & x = \frac{11}{357} & & \\ & V = \left\{ \frac{11}{357} \right\} & \\\end{align}\)