Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+140} & = & \color{red}{441x} +90 \\\Leftrightarrow & 945x \color{red}{+140} \color{blue}{-140} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-140} \\\Leftrightarrow & 945x-441x& = & 90-140 \\\Leftrightarrow & \color{red}{504} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{504} & & \\\Leftrightarrow & x = \frac{-25}{252} & & \\ & V = \left\{ \frac{-25}{252} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{8}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-8} & = & \color{red}{15x} +4 \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+8} \\\Leftrightarrow & -12x-15x& = & 4+8 \\\Leftrightarrow & \color{red}{-27} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-27} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{7})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-220} & = & \color{red}{-231x} +14 \\\Leftrightarrow & -1540x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +14 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -1540x+231x& = & 14+220 \\\Leftrightarrow & \color{red}{-1309} x& = & 234 \\\Leftrightarrow & x = \frac{234}{-1309} & & \\\Leftrightarrow & x = \frac{-234}{1309} & & \\ & V = \left\{ \frac{-234}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+48} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 168x \color{red}{+48} \color{blue}{-48} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-48} \\\Leftrightarrow & 168x+105x& = & 14-48 \\\Leftrightarrow & \color{red}{273} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{273} & & \\ & V = \left\{ \frac{-34}{273} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{12}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-12} & = & \color{red}{33x} +4 \\\Leftrightarrow & -88x \color{red}{-12} \color{blue}{+12} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{+12} \\\Leftrightarrow & -88x-33x& = & 4+12 \\\Leftrightarrow & \color{red}{-121} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-121} & & \\\Leftrightarrow & x = \frac{-16}{121} & & \\ & V = \left\{ \frac{-16}{121} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 4x-\frac{4}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x- \frac{8}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{-8} & = & \color{red}{18x} +27 \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{+8} \\\Leftrightarrow & 24x-18x& = & 27+8 \\\Leftrightarrow & \color{red}{6} x& = & 35 \\\Leftrightarrow & x = \frac{35}{6} & & \\ & V = \left\{ \frac{35}{6} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{8}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+16} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -132x \color{red}{+16} \color{blue}{-16} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{-16} \\\Leftrightarrow & -132x+154x& = & 99-16 \\\Leftrightarrow & \color{red}{22} x& = & 83 \\\Leftrightarrow & x = \frac{83}{22} & & \\ & V = \left\{ \frac{83}{22} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -3x+\frac{9}{5} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+30} & = & \color{red}{-105x} +63 \\\Leftrightarrow & 350x \color{red}{+30} \color{blue}{-30} \color{blue}{+105x} & = & \color{red}{-105x} +63 \color{blue}{+105x} \color{blue}{-30} \\\Leftrightarrow & 350x+105x& = & 63-30 \\\Leftrightarrow & \color{red}{455} x& = & 33 \\\Leftrightarrow & x = \frac{33}{455} & & \\ & V = \left\{ \frac{33}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{10})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{9}{10}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-99} & = & \color{red}{-550x} +50 \\\Leftrightarrow & 1320x \color{red}{-99} \color{blue}{+99} \color{blue}{+550x} & = & \color{red}{-550x} +50 \color{blue}{+550x} \color{blue}{+99} \\\Leftrightarrow & 1320x+550x& = & 50+99 \\\Leftrightarrow & \color{red}{1870} x& = & 149 \\\Leftrightarrow & x = \frac{149}{1870} & & \\ & V = \left\{ \frac{149}{1870} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 75x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 75x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{40} x& = & 18 \\\Leftrightarrow & x = \frac{18}{40} & & \\\Leftrightarrow & x = \frac{9}{20} & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{9}{5}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+27} & = & \color{red}{-120x} +10 \\\Leftrightarrow & -225x \color{red}{+27} \color{blue}{-27} \color{blue}{+120x} & = & \color{red}{-120x} +10 \color{blue}{+120x} \color{blue}{-27} \\\Leftrightarrow & -225x+120x& = & 10-27 \\\Leftrightarrow & \color{red}{-105} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-105} & & \\\Leftrightarrow & x = \frac{17}{105} & & \\ & V = \left\{ \frac{17}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{9})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{10}{9}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-110} & = & \color{red}{297x} +90 \\\Leftrightarrow & 990x \color{red}{-110} \color{blue}{+110} \color{blue}{-297x} & = & \color{red}{297x} +90 \color{blue}{-297x} \color{blue}{+110} \\\Leftrightarrow & 990x-297x& = & 90+110 \\\Leftrightarrow & \color{red}{693} x& = & 200 \\\Leftrightarrow & x = \frac{200}{693} & & \\ & V = \left\{ \frac{200}{693} \right\} & \\\end{align}\)