Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{175x} +40 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{+28} \\\Leftrightarrow & 210x-175x& = & 40+28 \\\Leftrightarrow & \color{red}{35} x& = & 68 \\\Leftrightarrow & x = \frac{68}{35} & & \\ & V = \left\{ \frac{68}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{20}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+60} & = & \color{red}{231x} +22 \\\Leftrightarrow & 330x \color{red}{+60} \color{blue}{-60} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-60} \\\Leftrightarrow & 330x-231x& = & 22-60 \\\Leftrightarrow & \color{red}{99} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{99} & & \\ & V = \left\{ \frac{-38}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{+144} & = & \color{red}{-616x} +77 \\\Leftrightarrow & -2640x \color{red}{+144} \color{blue}{-144} \color{blue}{+616x} & = & \color{red}{-616x} +77 \color{blue}{+616x} \color{blue}{-144} \\\Leftrightarrow & -2640x+616x& = & 77-144 \\\Leftrightarrow & \color{red}{-2024} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-2024} & & \\\Leftrightarrow & x = \frac{67}{2024} & & \\ & V = \left\{ \frac{67}{2024} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-198}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{-110x} +77 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & -198x+110x& = & 77+24 \\\Leftrightarrow & \color{red}{-88} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-88} & & \\\Leftrightarrow & x = \frac{-101}{88} & & \\ & V = \left\{ \frac{-101}{88} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-147x} +30 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{-140} \\\Leftrightarrow & 420x+147x& = & 30-140 \\\Leftrightarrow & \color{red}{567} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{567} & & \\ & V = \left\{ \frac{-110}{567} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{9})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-576}{ \color{blue}{72} }x- \frac{32}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -576x \color{red}{-32} & = & \color{red}{-648x} +27 \\\Leftrightarrow & -576x \color{red}{-32} \color{blue}{+32} \color{blue}{+648x} & = & \color{red}{-648x} +27 \color{blue}{+648x} \color{blue}{+32} \\\Leftrightarrow & -576x+648x& = & 27+32 \\\Leftrightarrow & \color{red}{72} x& = & 59 \\\Leftrightarrow & x = \frac{59}{72} & & \\ & V = \left\{ \frac{59}{72} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+100} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -240x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -240x+105x& = & 18-100 \\\Leftrightarrow & \color{red}{-135} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-135} & & \\\Leftrightarrow & x = \frac{82}{135} & & \\ & V = \left\{ \frac{82}{135} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{12})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 35x+\frac{35}{12}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+35} & = & \color{red}{96x} +54 \\\Leftrightarrow & 420x \color{red}{+35} \color{blue}{-35} \color{blue}{-96x} & = & \color{red}{96x} +54 \color{blue}{-96x} \color{blue}{-35} \\\Leftrightarrow & 420x-96x& = & 54-35 \\\Leftrightarrow & \color{red}{324} x& = & 19 \\\Leftrightarrow & x = \frac{19}{324} & & \\ & V = \left\{ \frac{19}{324} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{16x} +36 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-16x} & = & \color{red}{16x} +36 \color{blue}{-16x} \color{blue}{+21} \\\Leftrightarrow & 168x-16x& = & 36+21 \\\Leftrightarrow & \color{red}{152} x& = & 57 \\\Leftrightarrow & x = \frac{57}{152} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{+60} \\\Leftrightarrow & -420x+490x& = & 63+60 \\\Leftrightarrow & \color{red}{70} x& = & 123 \\\Leftrightarrow & x = \frac{123}{70} & & \\ & V = \left\{ \frac{123}{70} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{3})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 8x-\frac{16}{3}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x- \frac{128}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{-128} & = & \color{red}{-72x} +9 \\\Leftrightarrow & 192x \color{red}{-128} \color{blue}{+128} \color{blue}{+72x} & = & \color{red}{-72x} +9 \color{blue}{+72x} \color{blue}{+128} \\\Leftrightarrow & 192x+72x& = & 9+128 \\\Leftrightarrow & \color{red}{264} x& = & 137 \\\Leftrightarrow & x = \frac{137}{264} & & \\ & V = \left\{ \frac{137}{264} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{+32} & = & \color{red}{60x} +5 \\\Leftrightarrow & 96x \color{red}{+32} \color{blue}{-32} \color{blue}{-60x} & = & \color{red}{60x} +5 \color{blue}{-60x} \color{blue}{-32} \\\Leftrightarrow & 96x-60x& = & 5-32 \\\Leftrightarrow & \color{red}{36} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{36} & & \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)