Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{55x} +8 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & -132x-55x& = & 8+18 \\\Leftrightarrow & \color{red}{-187} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-187} & & \\\Leftrightarrow & x = \frac{-26}{187} & & \\ & V = \left\{ \frac{-26}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 14x-\frac{14}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{98}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-98} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1078x \color{red}{-98} \color{blue}{+98} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+98} \\\Leftrightarrow & 1078x+693x& = & 110+98 \\\Leftrightarrow & \color{red}{1771} x& = & 208 \\\Leftrightarrow & x = \frac{208}{1771} & & \\ & V = \left\{ \frac{208}{1771} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{35x} +6 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-24} \\\Leftrightarrow & -120x-35x& = & 6-24 \\\Leftrightarrow & \color{red}{-155} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-155} & & \\\Leftrightarrow & x = \frac{18}{155} & & \\ & V = \left\{ \frac{18}{155} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{96x} +16 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{-96x} & = & \color{red}{96x} +16 \color{blue}{-96x} \color{blue}{+45} \\\Leftrightarrow & -180x-96x& = & 16+45 \\\Leftrightarrow & \color{red}{-276} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-276} & & \\\Leftrightarrow & x = \frac{-61}{276} & & \\ & V = \left\{ \frac{-61}{276} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{11})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 9x-\frac{12}{11}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{792}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 792x \color{red}{-96} & = & \color{red}{-616x} +55 \\\Leftrightarrow & 792x \color{red}{-96} \color{blue}{+96} \color{blue}{+616x} & = & \color{red}{-616x} +55 \color{blue}{+616x} \color{blue}{+96} \\\Leftrightarrow & 792x+616x& = & 55+96 \\\Leftrightarrow & \color{red}{1408} x& = & 151 \\\Leftrightarrow & x = \frac{151}{1408} & & \\ & V = \left\{ \frac{151}{1408} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{1}{2})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{5}{2}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+35} & = & \color{red}{98x} +12 \\\Leftrightarrow & -140x \color{red}{+35} \color{blue}{-35} \color{blue}{-98x} & = & \color{red}{98x} +12 \color{blue}{-98x} \color{blue}{-35} \\\Leftrightarrow & -140x-98x& = & 12-35 \\\Leftrightarrow & \color{red}{-238} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-238} & & \\\Leftrightarrow & x = \frac{23}{238} & & \\ & V = \left\{ \frac{23}{238} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{4}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-225x} +10 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-36} \\\Leftrightarrow & 270x+225x& = & 10-36 \\\Leftrightarrow & \color{red}{495} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{495} & & \\ & V = \left\{ \frac{-26}{495} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{25}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{275}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-275} & = & \color{red}{-539x} +28 \\\Leftrightarrow & 1155x \color{red}{-275} \color{blue}{+275} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+275} \\\Leftrightarrow & 1155x+539x& = & 28+275 \\\Leftrightarrow & \color{red}{1694} x& = & 303 \\\Leftrightarrow & x = \frac{303}{1694} & & \\ & V = \left\{ \frac{303}{1694} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{36}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-36} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{-36} \color{blue}{+36} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+36} \\\Leftrightarrow & -336x-140x& = & 63+36 \\\Leftrightarrow & \color{red}{-476} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-476} & & \\\Leftrightarrow & x = \frac{-99}{476} & & \\ & V = \left\{ \frac{-99}{476} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{70x} +25 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -60x-70x& = & 25-12 \\\Leftrightarrow & \color{red}{-130} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-130} & & \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{6})& = & 8x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{100}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-100} & = & \color{red}{192x} +21 \\\Leftrightarrow & 360x \color{red}{-100} \color{blue}{+100} \color{blue}{-192x} & = & \color{red}{192x} +21 \color{blue}{-192x} \color{blue}{+100} \\\Leftrightarrow & 360x-192x& = & 21+100 \\\Leftrightarrow & \color{red}{168} x& = & 121 \\\Leftrightarrow & x = \frac{121}{168} & & \\ & V = \left\{ \frac{121}{168} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{320x} +16 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{-320x} & = & \color{red}{320x} +16 \color{blue}{-320x} \color{blue}{+105} \\\Leftrightarrow & -840x-320x& = & 16+105 \\\Leftrightarrow & \color{red}{-1160} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-1160} & & \\\Leftrightarrow & x = \frac{-121}{1160} & & \\ & V = \left\{ \frac{-121}{1160} \right\} & \\\end{align}\)