Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{15}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{-98x} +63 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-30} \\\Leftrightarrow & 84x+98x& = & 63-30 \\\Leftrightarrow & \color{red}{182} x& = & 33 \\\Leftrightarrow & x = \frac{33}{182} & & \\ & V = \left\{ \frac{33}{182} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & 6x+\frac{3}{10} \\\Leftrightarrow & -25x-\frac{15}{2}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{60}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{-75} & = & \color{red}{60x} +3 \\\Leftrightarrow & -250x \color{red}{-75} \color{blue}{+75} \color{blue}{-60x} & = & \color{red}{60x} +3 \color{blue}{-60x} \color{blue}{+75} \\\Leftrightarrow & -250x-60x& = & 3+75 \\\Leftrightarrow & \color{red}{-310} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-310} & & \\\Leftrightarrow & x = \frac{-39}{155} & & \\ & V = \left\{ \frac{-39}{155} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-80} & = & \color{red}{140x} +21 \\\Leftrightarrow & -336x \color{red}{-80} \color{blue}{+80} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{+80} \\\Leftrightarrow & -336x-140x& = & 21+80 \\\Leftrightarrow & \color{red}{-476} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-476} & & \\\Leftrightarrow & x = \frac{-101}{476} & & \\ & V = \left\{ \frac{-101}{476} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{245x} +49 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{-30} \\\Leftrightarrow & -210x-245x& = & 49-30 \\\Leftrightarrow & \color{red}{-455} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-455} & & \\\Leftrightarrow & x = \frac{-19}{455} & & \\ & V = \left\{ \frac{-19}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -9x+\frac{6}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+30} & = & \color{red}{-275x} +44 \\\Leftrightarrow & -495x \color{red}{+30} \color{blue}{-30} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{-30} \\\Leftrightarrow & -495x+275x& = & 44-30 \\\Leftrightarrow & \color{red}{-220} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-220} & & \\\Leftrightarrow & x = \frac{-7}{110} & & \\ & V = \left\{ \frac{-7}{110} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 3x+\frac{5}{3} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-48} & = & \color{red}{63x} +35 \\\Leftrightarrow & -168x \color{red}{-48} \color{blue}{+48} \color{blue}{-63x} & = & \color{red}{63x} +35 \color{blue}{-63x} \color{blue}{+48} \\\Leftrightarrow & -168x-63x& = & 35+48 \\\Leftrightarrow & \color{red}{-231} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-231} & & \\\Leftrightarrow & x = \frac{-83}{231} & & \\ & V = \left\{ \frac{-83}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{10})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -21x+\frac{21}{10}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-210}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -210x \color{red}{+21} & = & \color{red}{-80x} +15 \\\Leftrightarrow & -210x \color{red}{+21} \color{blue}{-21} \color{blue}{+80x} & = & \color{red}{-80x} +15 \color{blue}{+80x} \color{blue}{-21} \\\Leftrightarrow & -210x+80x& = & 15-21 \\\Leftrightarrow & \color{red}{-130} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-130} & & \\\Leftrightarrow & x = \frac{3}{65} & & \\ & V = \left\{ \frac{3}{65} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 20x-\frac{12}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-108} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 1260x \color{red}{-108} \color{blue}{+108} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+108} \\\Leftrightarrow & 1260x+441x& = & 56+108 \\\Leftrightarrow & \color{red}{1701} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1701} & & \\ & V = \left\{ \frac{164}{1701} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{27x} +2 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+28} \\\Leftrightarrow & 126x-27x& = & 2+28 \\\Leftrightarrow & \color{red}{99} x& = & 30 \\\Leftrightarrow & x = \frac{30}{99} & & \\\Leftrightarrow & x = \frac{10}{33} & & \\ & V = \left\{ \frac{10}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{7})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{20}{7}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+20} & = & \color{red}{-56x} +4 \\\Leftrightarrow & -105x \color{red}{+20} \color{blue}{-20} \color{blue}{+56x} & = & \color{red}{-56x} +4 \color{blue}{+56x} \color{blue}{-20} \\\Leftrightarrow & -105x+56x& = & 4-20 \\\Leftrightarrow & \color{red}{-49} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-49} & & \\\Leftrightarrow & x = \frac{16}{49} & & \\ & V = \left\{ \frac{16}{49} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -6x+\frac{5}{6} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -6x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-36x} +5 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{+28} \\\Leftrightarrow & 210x+36x& = & 5+28 \\\Leftrightarrow & \color{red}{246} x& = & 33 \\\Leftrightarrow & x = \frac{33}{246} & & \\\Leftrightarrow & x = \frac{11}{82} & & \\ & V = \left\{ \frac{11}{82} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & 450x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 450x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{345} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{345} & & \\ & V = \left\{ \frac{-26}{345} \right\} & \\\end{align}\)