Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+16} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 112x \color{red}{+16} \color{blue}{-16} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-16} \\\Leftrightarrow & 112x+70x& = & 63-16 \\\Leftrightarrow & \color{red}{182} x& = & 47 \\\Leftrightarrow & x = \frac{47}{182} & & \\ & V = \left\{ \frac{47}{182} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-270} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1188x \color{red}{-270} \color{blue}{+270} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+270} \\\Leftrightarrow & -1188x-495x& = & 88+270 \\\Leftrightarrow & \color{red}{-1683} x& = & 358 \\\Leftrightarrow & x = \frac{358}{-1683} & & \\\Leftrightarrow & x = \frac{-358}{1683} & & \\ & V = \left\{ \frac{-358}{1683} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{-135} & = & \color{red}{-252x} +32 \\\Leftrightarrow & -216x \color{red}{-135} \color{blue}{+135} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{+135} \\\Leftrightarrow & -216x+252x& = & 32+135 \\\Leftrightarrow & \color{red}{36} x& = & 167 \\\Leftrightarrow & x = \frac{167}{36} & & \\ & V = \left\{ \frac{167}{36} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +45 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 45-132 \\\Leftrightarrow & \color{red}{935} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{935} & & \\ & V = \left\{ \frac{-87}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-108} & = & \color{red}{225x} +40 \\\Leftrightarrow & -405x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & -405x-225x& = & 40+108 \\\Leftrightarrow & \color{red}{-630} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-630} & & \\\Leftrightarrow & x = \frac{-74}{315} & & \\ & V = \left\{ \frac{-74}{315} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 9x+\frac{7}{6} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{54x} +7 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +7 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & 210x-54x& = & 7+28 \\\Leftrightarrow & \color{red}{156} x& = & 35 \\\Leftrightarrow & x = \frac{35}{156} & & \\ & V = \left\{ \frac{35}{156} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{16}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{45x} +18 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{+80} \\\Leftrightarrow & 240x-45x& = & 18+80 \\\Leftrightarrow & \color{red}{195} x& = & 98 \\\Leftrightarrow & x = \frac{98}{195} & & \\ & V = \left\{ \frac{98}{195} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & -3x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{10}{3}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-50} & = & \color{red}{-45x} +27 \\\Leftrightarrow & -120x \color{red}{-50} \color{blue}{+50} \color{blue}{+45x} & = & \color{red}{-45x} +27 \color{blue}{+45x} \color{blue}{+50} \\\Leftrightarrow & -120x+45x& = & 27+50 \\\Leftrightarrow & \color{red}{-75} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-75} & & \\\Leftrightarrow & x = \frac{-77}{75} & & \\ & V = \left\{ \frac{-77}{75} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{15}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-45} & = & \color{red}{147x} +56 \\\Leftrightarrow & -420x \color{red}{-45} \color{blue}{+45} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+45} \\\Leftrightarrow & -420x-147x& = & 56+45 \\\Leftrightarrow & \color{red}{-567} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-567} & & \\\Leftrightarrow & x = \frac{-101}{567} & & \\ & V = \left\{ \frac{-101}{567} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{50}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 50x \color{red}{+4} & = & \color{red}{-45x} +6 \\\Leftrightarrow & 50x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & 50x+45x& = & 6-4 \\\Leftrightarrow & \color{red}{95} x& = & 2 \\\Leftrightarrow & x = \frac{2}{95} & & \\ & V = \left\{ \frac{2}{95} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+44} & = & \color{red}{495x} +50 \\\Leftrightarrow & -220x \color{red}{+44} \color{blue}{-44} \color{blue}{-495x} & = & \color{red}{495x} +50 \color{blue}{-495x} \color{blue}{-44} \\\Leftrightarrow & -220x-495x& = & 50-44 \\\Leftrightarrow & \color{red}{-715} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-715} & & \\\Leftrightarrow & x = \frac{-6}{715} & & \\ & V = \left\{ \frac{-6}{715} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{-63x} +24 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-20} \\\Leftrightarrow & -180x+63x& = & 24-20 \\\Leftrightarrow & \color{red}{-117} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-117} & & \\\Leftrightarrow & x = \frac{-4}{117} & & \\ & V = \left\{ \frac{-4}{117} \right\} & \\\end{align}\)