Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{8}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-88} & = & \color{red}{275x} +10 \\\Leftrightarrow & -660x \color{red}{-88} \color{blue}{+88} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+88} \\\Leftrightarrow & -660x-275x& = & 10+88 \\\Leftrightarrow & \color{red}{-935} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-935} & & \\\Leftrightarrow & x = \frac{-98}{935} & & \\ & V = \left\{ \frac{-98}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{20}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-20} & = & \color{red}{-21x} +4 \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & -30x+21x& = & 4+20 \\\Leftrightarrow & \color{red}{-9} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-9} & & \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -8x+\frac{4}{5} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-12} & = & \color{red}{-40x} +4 \\\Leftrightarrow & 45x \color{red}{-12} \color{blue}{+12} \color{blue}{+40x} & = & \color{red}{-40x} +4 \color{blue}{+40x} \color{blue}{+12} \\\Leftrightarrow & 45x+40x& = & 4+12 \\\Leftrightarrow & \color{red}{85} x& = & 16 \\\Leftrightarrow & x = \frac{16}{85} & & \\ & V = \left\{ \frac{16}{85} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+32} & = & \color{red}{252x} +27 \\\Leftrightarrow & -216x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +27 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -216x-252x& = & 27-32 \\\Leftrightarrow & \color{red}{-468} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-468} & & \\\Leftrightarrow & x = \frac{5}{468} & & \\ & V = \left\{ \frac{5}{468} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 24x-\frac{24}{5}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-48} & = & \color{red}{50x} +7 \\\Leftrightarrow & 240x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +7 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & 240x-50x& = & 7+48 \\\Leftrightarrow & \color{red}{190} x& = & 55 \\\Leftrightarrow & x = \frac{55}{190} & & \\\Leftrightarrow & x = \frac{11}{38} & & \\ & V = \left\{ \frac{11}{38} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{-8} & = & \color{red}{-90x} +45 \\\Leftrightarrow & 108x \color{red}{-8} \color{blue}{+8} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+8} \\\Leftrightarrow & 108x+90x& = & 45+8 \\\Leftrightarrow & \color{red}{198} x& = & 53 \\\Leftrightarrow & x = \frac{53}{198} & & \\ & V = \left\{ \frac{53}{198} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-140} & = & \color{red}{-189x} +27 \\\Leftrightarrow & -168x \color{red}{-140} \color{blue}{+140} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{+140} \\\Leftrightarrow & -168x+189x& = & 27+140 \\\Leftrightarrow & \color{red}{21} x& = & 167 \\\Leftrightarrow & x = \frac{167}{21} & & \\ & V = \left\{ \frac{167}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x+ \frac{120}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{350x} +21 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{-120} \\\Leftrightarrow & 840x-350x& = & 21-120 \\\Leftrightarrow & \color{red}{490} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{490} & & \\ & V = \left\{ \frac{-99}{490} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & 180x+105x& = & 18+40 \\\Leftrightarrow & \color{red}{285} x& = & 58 \\\Leftrightarrow & x = \frac{58}{285} & & \\ & V = \left\{ \frac{58}{285} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -10x+\frac{4}{3}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+16} & = & \color{red}{-84x} +27 \\\Leftrightarrow & -120x \color{red}{+16} \color{blue}{-16} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{-16} \\\Leftrightarrow & -120x+84x& = & 27-16 \\\Leftrightarrow & \color{red}{-36} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-36} & & \\\Leftrightarrow & x = \frac{-11}{36} & & \\ & V = \left\{ \frac{-11}{36} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2112}{ \color{blue}{88} }x+ \frac{192}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2112x \color{red}{+192} & = & \color{red}{440x} +99 \\\Leftrightarrow & 2112x \color{red}{+192} \color{blue}{-192} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{-192} \\\Leftrightarrow & 2112x-440x& = & 99-192 \\\Leftrightarrow & \color{red}{1672} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1672} & & \\ & V = \left\{ \frac{-93}{1672} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1440}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1440x \color{red}{+64} & = & \color{red}{-504x} +45 \\\Leftrightarrow & 1440x \color{red}{+64} \color{blue}{-64} \color{blue}{+504x} & = & \color{red}{-504x} +45 \color{blue}{+504x} \color{blue}{-64} \\\Leftrightarrow & 1440x+504x& = & 45-64 \\\Leftrightarrow & \color{red}{1944} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{1944} & & \\ & V = \left\{ \frac{-19}{1944} \right\} & \\\end{align}\)