Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{11})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 21x+\frac{21}{11}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 231x \color{red}{+21} & = & \color{red}{22x} +3 \\\Leftrightarrow & 231x \color{red}{+21} \color{blue}{-21} \color{blue}{-22x} & = & \color{red}{22x} +3 \color{blue}{-22x} \color{blue}{-21} \\\Leftrightarrow & 231x-22x& = & 3-21 \\\Leftrightarrow & \color{red}{209} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{209} & & \\ & V = \left\{ \frac{-18}{209} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-66} & = & \color{red}{385x} +49 \\\Leftrightarrow & -924x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -924x-385x& = & 49+66 \\\Leftrightarrow & \color{red}{-1309} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-1309} & & \\\Leftrightarrow & x = \frac{-115}{1309} & & \\ & V = \left\{ \frac{-115}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{54x} +5 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-54x} & = & \color{red}{54x} +5 \color{blue}{-54x} \color{blue}{-16} \\\Leftrightarrow & -24x-54x& = & 5-16 \\\Leftrightarrow & \color{red}{-78} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-78} & & \\\Leftrightarrow & x = \frac{11}{78} & & \\ & V = \left\{ \frac{11}{78} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{5})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 20x+\frac{16}{5}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{16}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+16} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 100x \color{red}{+16} \color{blue}{-16} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-16} \\\Leftrightarrow & 100x+35x& = & 3-16 \\\Leftrightarrow & \color{red}{135} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{135} & & \\ & V = \left\{ \frac{-13}{135} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 4x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 4x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+196} & = & \color{red}{140x} +30 \\\Leftrightarrow & 735x \color{red}{+196} \color{blue}{-196} \color{blue}{-140x} & = & \color{red}{140x} +30 \color{blue}{-140x} \color{blue}{-196} \\\Leftrightarrow & 735x-140x& = & 30-196 \\\Leftrightarrow & \color{red}{595} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{595} & & \\ & V = \left\{ \frac{-166}{595} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & -9x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+16} & = & \color{red}{-63x} +2 \\\Leftrightarrow & 56x \color{red}{+16} \color{blue}{-16} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-16} \\\Leftrightarrow & 56x+63x& = & 2-16 \\\Leftrightarrow & \color{red}{119} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{119} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-72} & = & \color{red}{105x} +20 \\\Leftrightarrow & -270x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & -270x-105x& = & 20+72 \\\Leftrightarrow & \color{red}{-375} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-375} & & \\\Leftrightarrow & x = \frac{-92}{375} & & \\ & V = \left\{ \frac{-92}{375} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+66} & = & \color{red}{539x} +28 \\\Leftrightarrow & 308x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & 308x-539x& = & 28-66 \\\Leftrightarrow & \color{red}{-231} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-231} & & \\\Leftrightarrow & x = \frac{38}{231} & & \\ & V = \left\{ \frac{38}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+42} & = & \color{red}{45x} +8 \\\Leftrightarrow & 252x \color{red}{+42} \color{blue}{-42} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-42} \\\Leftrightarrow & 252x-45x& = & 8-42 \\\Leftrightarrow & \color{red}{207} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{207} & & \\ & V = \left\{ \frac{-34}{207} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{9})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{4}{9}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+28} & = & \color{red}{315x} +90 \\\Leftrightarrow & -252x \color{red}{+28} \color{blue}{-28} \color{blue}{-315x} & = & \color{red}{315x} +90 \color{blue}{-315x} \color{blue}{-28} \\\Leftrightarrow & -252x-315x& = & 90-28 \\\Leftrightarrow & \color{red}{-567} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-567} & & \\\Leftrightarrow & x = \frac{-62}{567} & & \\ & V = \left\{ \frac{-62}{567} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{8})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 10x-\frac{15}{8}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{-45} & = & \color{red}{-168x} +20 \\\Leftrightarrow & 240x \color{red}{-45} \color{blue}{+45} \color{blue}{+168x} & = & \color{red}{-168x} +20 \color{blue}{+168x} \color{blue}{+45} \\\Leftrightarrow & 240x+168x& = & 20+45 \\\Leftrightarrow & \color{red}{408} x& = & 65 \\\Leftrightarrow & x = \frac{65}{408} & & \\ & V = \left\{ \frac{65}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{7}{4} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-48} & = & \color{red}{-80x} +35 \\\Leftrightarrow & -300x \color{red}{-48} \color{blue}{+48} \color{blue}{+80x} & = & \color{red}{-80x} +35 \color{blue}{+80x} \color{blue}{+48} \\\Leftrightarrow & -300x+80x& = & 35+48 \\\Leftrightarrow & \color{red}{-220} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-220} & & \\\Leftrightarrow & x = \frac{-83}{220} & & \\ & V = \left\{ \frac{-83}{220} \right\} & \\\end{align}\)