Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 60x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{25} x& = & 18 \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+40} & = & \color{red}{-42x} +21 \\\Leftrightarrow & -112x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & -112x+42x& = & 21-40 \\\Leftrightarrow & \color{red}{-70} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-70} & & \\\Leftrightarrow & x = \frac{19}{70} & & \\ & V = \left\{ \frac{19}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-840}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -840x \color{red}{+120} & = & \color{red}{-588x} +49 \\\Leftrightarrow & -840x \color{red}{+120} \color{blue}{-120} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{-120} \\\Leftrightarrow & -840x+588x& = & 49-120 \\\Leftrightarrow & \color{red}{-252} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-252} & & \\\Leftrightarrow & x = \frac{71}{252} & & \\ & V = \left\{ \frac{71}{252} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{12})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x+ \frac{75}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{+75} & = & \color{red}{-252x} +20 \\\Leftrightarrow & 720x \color{red}{+75} \color{blue}{-75} \color{blue}{+252x} & = & \color{red}{-252x} +20 \color{blue}{+252x} \color{blue}{-75} \\\Leftrightarrow & 720x+252x& = & 20-75 \\\Leftrightarrow & \color{red}{972} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{972} & & \\ & V = \left\{ \frac{-55}{972} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{891x} +77 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{-891x} & = & \color{red}{891x} +77 \color{blue}{-891x} \color{blue}{+90} \\\Leftrightarrow & 990x-891x& = & 77+90 \\\Leftrightarrow & \color{red}{99} x& = & 167 \\\Leftrightarrow & x = \frac{167}{99} & & \\ & V = \left\{ \frac{167}{99} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & -9x+\frac{9}{5} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+100} & = & \color{red}{-495x} +99 \\\Leftrightarrow & 1100x \color{red}{+100} \color{blue}{-100} \color{blue}{+495x} & = & \color{red}{-495x} +99 \color{blue}{+495x} \color{blue}{-100} \\\Leftrightarrow & 1100x+495x& = & 99-100 \\\Leftrightarrow & \color{red}{1595} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1595} & & \\ & V = \left\{ \frac{-1}{1595} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{1}{3})& = & 8x+\frac{7}{8} \\\Leftrightarrow & 35x-\frac{7}{3}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x- \frac{56}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{-56} & = & \color{red}{192x} +21 \\\Leftrightarrow & 840x \color{red}{-56} \color{blue}{+56} \color{blue}{-192x} & = & \color{red}{192x} +21 \color{blue}{-192x} \color{blue}{+56} \\\Leftrightarrow & 840x-192x& = & 21+56 \\\Leftrightarrow & \color{red}{648} x& = & 77 \\\Leftrightarrow & x = \frac{77}{648} & & \\ & V = \left\{ \frac{77}{648} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+135} & = & \color{red}{-180x} +8 \\\Leftrightarrow & -432x \color{red}{+135} \color{blue}{-135} \color{blue}{+180x} & = & \color{red}{-180x} +8 \color{blue}{+180x} \color{blue}{-135} \\\Leftrightarrow & -432x+180x& = & 8-135 \\\Leftrightarrow & \color{red}{-252} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-252} & & \\\Leftrightarrow & x = \frac{127}{252} & & \\ & V = \left\{ \frac{127}{252} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{7})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 35x+4& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{40}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+40} & = & \color{red}{20x} +9 \\\Leftrightarrow & 350x \color{red}{+40} \color{blue}{-40} \color{blue}{-20x} & = & \color{red}{20x} +9 \color{blue}{-20x} \color{blue}{-40} \\\Leftrightarrow & 350x-20x& = & 9-40 \\\Leftrightarrow & \color{red}{330} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{330} & & \\ & V = \left\{ \frac{-31}{330} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{2})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{9}{2}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{+27} & = & \color{red}{42x} +4 \\\Leftrightarrow & 90x \color{red}{+27} \color{blue}{-27} \color{blue}{-42x} & = & \color{red}{42x} +4 \color{blue}{-42x} \color{blue}{-27} \\\Leftrightarrow & 90x-42x& = & 4-27 \\\Leftrightarrow & \color{red}{48} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{48} & & \\ & V = \left\{ \frac{-23}{48} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & -3x+\frac{5}{7} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{-63x} +15 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +15 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & -420x+63x& = & 15-140 \\\Leftrightarrow & \color{red}{-357} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-357} & & \\\Leftrightarrow & x = \frac{125}{357} & & \\ & V = \left\{ \frac{125}{357} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & 2x+\frac{3}{8} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 2x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1800}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{144}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1800x \color{red}{-160} & = & \color{red}{144x} +27 \\\Leftrightarrow & -1800x \color{red}{-160} \color{blue}{+160} \color{blue}{-144x} & = & \color{red}{144x} +27 \color{blue}{-144x} \color{blue}{+160} \\\Leftrightarrow & -1800x-144x& = & 27+160 \\\Leftrightarrow & \color{red}{-1944} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-1944} & & \\\Leftrightarrow & x = \frac{-187}{1944} & & \\ & V = \left\{ \frac{-187}{1944} \right\} & \\\end{align}\)