Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & -2x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-198}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-162} & = & \color{red}{-198x} +110 \\\Leftrightarrow & -1782x \color{red}{-162} \color{blue}{+162} \color{blue}{+198x} & = & \color{red}{-198x} +110 \color{blue}{+198x} \color{blue}{+162} \\\Leftrightarrow & -1782x+198x& = & 110+162 \\\Leftrightarrow & \color{red}{-1584} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-1584} & & \\\Leftrightarrow & x = \frac{-17}{99} & & \\ & V = \left\{ \frac{-17}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{9})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 12x+\frac{8}{9}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+56} & = & \color{red}{315x} +45 \\\Leftrightarrow & 756x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & 756x-315x& = & 45-56 \\\Leftrightarrow & \color{red}{441} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{441} & & \\ & V = \left\{ \frac{-11}{441} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1512}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1512x \color{red}{-189} & = & \color{red}{-360x} +16 \\\Leftrightarrow & 1512x \color{red}{-189} \color{blue}{+189} \color{blue}{+360x} & = & \color{red}{-360x} +16 \color{blue}{+360x} \color{blue}{+189} \\\Leftrightarrow & 1512x+360x& = & 16+189 \\\Leftrightarrow & \color{red}{1872} x& = & 205 \\\Leftrightarrow & x = \frac{205}{1872} & & \\ & V = \left\{ \frac{205}{1872} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{4})& = & -2x+\frac{3}{8} \\\Leftrightarrow & 9x+\frac{15}{4}& = & -2x+\frac{3}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{+30} & = & \color{red}{-16x} +3 \\\Leftrightarrow & 72x \color{red}{+30} \color{blue}{-30} \color{blue}{+16x} & = & \color{red}{-16x} +3 \color{blue}{+16x} \color{blue}{-30} \\\Leftrightarrow & 72x+16x& = & 3-30 \\\Leftrightarrow & \color{red}{88} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{88} & & \\ & V = \left\{ \frac{-27}{88} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -2x+\frac{9}{4} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{-40x} +45 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{+40x} & = & \color{red}{-40x} +45 \color{blue}{+40x} \color{blue}{+48} \\\Leftrightarrow & 180x+40x& = & 45+48 \\\Leftrightarrow & \color{red}{220} x& = & 93 \\\Leftrightarrow & x = \frac{93}{220} & & \\ & V = \left\{ \frac{93}{220} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{9})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+40} & = & \color{red}{225x} +81 \\\Leftrightarrow & 270x \color{red}{+40} \color{blue}{-40} \color{blue}{-225x} & = & \color{red}{225x} +81 \color{blue}{-225x} \color{blue}{-40} \\\Leftrightarrow & 270x-225x& = & 81-40 \\\Leftrightarrow & \color{red}{45} x& = & 41 \\\Leftrightarrow & x = \frac{41}{45} & & \\ & V = \left\{ \frac{41}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+14} & = & \color{red}{9x} +2 \\\Leftrightarrow & -42x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & -42x-9x& = & 2-14 \\\Leftrightarrow & \color{red}{-51} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-51} & & \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-16} & = & \color{red}{77x} +3 \\\Leftrightarrow & 220x \color{red}{-16} \color{blue}{+16} \color{blue}{-77x} & = & \color{red}{77x} +3 \color{blue}{-77x} \color{blue}{+16} \\\Leftrightarrow & 220x-77x& = & 3+16 \\\Leftrightarrow & \color{red}{143} x& = & 19 \\\Leftrightarrow & x = \frac{19}{143} & & \\ & V = \left\{ \frac{19}{143} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+140} & = & \color{red}{-105x} +27 \\\Leftrightarrow & 336x \color{red}{+140} \color{blue}{-140} \color{blue}{+105x} & = & \color{red}{-105x} +27 \color{blue}{+105x} \color{blue}{-140} \\\Leftrightarrow & 336x+105x& = & 27-140 \\\Leftrightarrow & \color{red}{441} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{441} & & \\ & V = \left\{ \frac{-113}{441} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{105x} +20 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -360x-105x& = & 20+36 \\\Leftrightarrow & \color{red}{-465} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-465} & & \\\Leftrightarrow & x = \frac{-56}{465} & & \\ & V = \left\{ \frac{-56}{465} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -30x+\frac{24}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x+ \frac{144}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{+144} & = & \color{red}{294x} +35 \\\Leftrightarrow & -1260x \color{red}{+144} \color{blue}{-144} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-144} \\\Leftrightarrow & -1260x-294x& = & 35-144 \\\Leftrightarrow & \color{red}{-1554} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1554} & & \\\Leftrightarrow & x = \frac{109}{1554} & & \\ & V = \left\{ \frac{109}{1554} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+12} & = & \color{red}{-99x} +5 \\\Leftrightarrow & -88x \color{red}{+12} \color{blue}{-12} \color{blue}{+99x} & = & \color{red}{-99x} +5 \color{blue}{+99x} \color{blue}{-12} \\\Leftrightarrow & -88x+99x& = & 5-12 \\\Leftrightarrow & \color{red}{11} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)