Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 8x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{560}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{-60} & = & \color{red}{560x} +63 \\\Leftrightarrow & 1050x \color{red}{-60} \color{blue}{+60} \color{blue}{-560x} & = & \color{red}{560x} +63 \color{blue}{-560x} \color{blue}{+60} \\\Leftrightarrow & 1050x-560x& = & 63+60 \\\Leftrightarrow & \color{red}{490} x& = & 123 \\\Leftrightarrow & x = \frac{123}{490} & & \\ & V = \left\{ \frac{123}{490} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{5})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{-120x} +10 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{+120x} & = & \color{red}{-120x} +10 \color{blue}{+120x} \color{blue}{-42} \\\Leftrightarrow & 315x+120x& = & 10-42 \\\Leftrightarrow & \color{red}{435} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{435} & & \\ & V = \left\{ \frac{-32}{435} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{3})& = & 6x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{20}{3}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{+100} & = & \color{red}{90x} +18 \\\Leftrightarrow & 375x \color{red}{+100} \color{blue}{-100} \color{blue}{-90x} & = & \color{red}{90x} +18 \color{blue}{-90x} \color{blue}{-100} \\\Leftrightarrow & 375x-90x& = & 18-100 \\\Leftrightarrow & \color{red}{285} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{285} & & \\ & V = \left\{ \frac{-82}{285} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+54} & = & \color{red}{-90x} +50 \\\Leftrightarrow & 675x \color{red}{+54} \color{blue}{-54} \color{blue}{+90x} & = & \color{red}{-90x} +50 \color{blue}{+90x} \color{blue}{-54} \\\Leftrightarrow & 675x+90x& = & 50-54 \\\Leftrightarrow & \color{red}{765} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{765} & & \\ & V = \left\{ \frac{-4}{765} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-245x} +50 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 420x+245x& = & 50+84 \\\Leftrightarrow & \color{red}{665} x& = & 134 \\\Leftrightarrow & x = \frac{134}{665} & & \\ & V = \left\{ \frac{134}{665} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+48} & = & \color{red}{-140x} +45 \\\Leftrightarrow & -400x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & -400x+140x& = & 45-48 \\\Leftrightarrow & \color{red}{-260} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-260} & & \\\Leftrightarrow & x = \frac{3}{260} & & \\ & V = \left\{ \frac{3}{260} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{8}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{+16} & = & \color{red}{70x} +45 \\\Leftrightarrow & 40x \color{red}{+16} \color{blue}{-16} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-16} \\\Leftrightarrow & 40x-70x& = & 45-16 \\\Leftrightarrow & \color{red}{-30} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-30} & & \\\Leftrightarrow & x = \frac{-29}{30} & & \\ & V = \left\{ \frac{-29}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-20x} +15 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+20x} & = & \color{red}{-20x} +15 \color{blue}{+20x} \color{blue}{-24} \\\Leftrightarrow & 90x+20x& = & 15-24 \\\Leftrightarrow & \color{red}{110} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{110} & & \\ & V = \left\{ \frac{-9}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & 3x+\frac{5}{9} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 3x+\frac{5}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1440}{ \color{blue}{72} }x+ \frac{225}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{40}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1440x \color{red}{+225} & = & \color{red}{216x} +40 \\\Leftrightarrow & 1440x \color{red}{+225} \color{blue}{-225} \color{blue}{-216x} & = & \color{red}{216x} +40 \color{blue}{-216x} \color{blue}{-225} \\\Leftrightarrow & 1440x-216x& = & 40-225 \\\Leftrightarrow & \color{red}{1224} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{1224} & & \\ & V = \left\{ \frac{-185}{1224} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{70} x& = & 21 \\\Leftrightarrow & x = \frac{21}{70} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & 3x+\frac{5}{9} \\\Leftrightarrow & 8x+\frac{12}{11}& = & 3x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+108} & = & \color{red}{297x} +55 \\\Leftrightarrow & 792x \color{red}{+108} \color{blue}{-108} \color{blue}{-297x} & = & \color{red}{297x} +55 \color{blue}{-297x} \color{blue}{-108} \\\Leftrightarrow & 792x-297x& = & 55-108 \\\Leftrightarrow & \color{red}{495} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{495} & & \\ & V = \left\{ \frac{-53}{495} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3960}{ \color{blue}{132} }x+ \frac{216}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3960x \color{red}{+216} & = & \color{red}{924x} +55 \\\Leftrightarrow & -3960x \color{red}{+216} \color{blue}{-216} \color{blue}{-924x} & = & \color{red}{924x} +55 \color{blue}{-924x} \color{blue}{-216} \\\Leftrightarrow & -3960x-924x& = & 55-216 \\\Leftrightarrow & \color{red}{-4884} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{-4884} & & \\\Leftrightarrow & x = \frac{161}{4884} & & \\ & V = \left\{ \frac{161}{4884} \right\} & \\\end{align}\)