Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-882}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -882x \color{red}{-196} & = & \color{red}{-189x} +72 \\\Leftrightarrow & -882x \color{red}{-196} \color{blue}{+196} \color{blue}{+189x} & = & \color{red}{-189x} +72 \color{blue}{+189x} \color{blue}{+196} \\\Leftrightarrow & -882x+189x& = & 72+196 \\\Leftrightarrow & \color{red}{-693} x& = & 268 \\\Leftrightarrow & x = \frac{268}{-693} & & \\\Leftrightarrow & x = \frac{-268}{693} & & \\ & V = \left\{ \frac{-268}{693} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 16x+\frac{16}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+176} & = & \color{red}{-99x} +24 \\\Leftrightarrow & 528x \color{red}{+176} \color{blue}{-176} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{-176} \\\Leftrightarrow & 528x+99x& = & 24-176 \\\Leftrightarrow & \color{red}{627} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{627} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+63} & = & \color{red}{192x} +32 \\\Leftrightarrow & -504x \color{red}{+63} \color{blue}{-63} \color{blue}{-192x} & = & \color{red}{192x} +32 \color{blue}{-192x} \color{blue}{-63} \\\Leftrightarrow & -504x-192x& = & 32-63 \\\Leftrightarrow & \color{red}{-696} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-696} & & \\\Leftrightarrow & x = \frac{31}{696} & & \\ & V = \left\{ \frac{31}{696} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{-45x} +30 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{+45x} & = & \color{red}{-45x} +30 \color{blue}{+45x} \color{blue}{-8} \\\Leftrightarrow & -36x+45x& = & 30-8 \\\Leftrightarrow & \color{red}{9} x& = & 22 \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{2})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -35x-\frac{35}{2}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-490}{ \color{blue}{14} }x- \frac{245}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -490x \color{red}{-245} & = & \color{red}{42x} +12 \\\Leftrightarrow & -490x \color{red}{-245} \color{blue}{+245} \color{blue}{-42x} & = & \color{red}{42x} +12 \color{blue}{-42x} \color{blue}{+245} \\\Leftrightarrow & -490x-42x& = & 12+245 \\\Leftrightarrow & \color{red}{-532} x& = & 257 \\\Leftrightarrow & x = \frac{257}{-532} & & \\\Leftrightarrow & x = \frac{-257}{532} & & \\ & V = \left\{ \frac{-257}{532} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{11})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 8x+\frac{6}{11}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+18} & = & \color{red}{99x} +77 \\\Leftrightarrow & 264x \color{red}{+18} \color{blue}{-18} \color{blue}{-99x} & = & \color{red}{99x} +77 \color{blue}{-99x} \color{blue}{-18} \\\Leftrightarrow & 264x-99x& = & 77-18 \\\Leftrightarrow & \color{red}{165} x& = & 59 \\\Leftrightarrow & x = \frac{59}{165} & & \\ & V = \left\{ \frac{59}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{-120x} +35 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{+36} \\\Leftrightarrow & -225x+120x& = & 35+36 \\\Leftrightarrow & \color{red}{-105} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-105} & & \\\Leftrightarrow & x = \frac{-71}{105} & & \\ & V = \left\{ \frac{-71}{105} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-75} & = & \color{red}{100x} +16 \\\Leftrightarrow & -180x \color{red}{-75} \color{blue}{+75} \color{blue}{-100x} & = & \color{red}{100x} +16 \color{blue}{-100x} \color{blue}{+75} \\\Leftrightarrow & -180x-100x& = & 16+75 \\\Leftrightarrow & \color{red}{-280} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-280} & & \\\Leftrightarrow & x = \frac{-13}{40} & & \\ & V = \left\{ \frac{-13}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{3})& = & 6x+\frac{3}{4} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 6x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+56} & = & \color{red}{72x} +9 \\\Leftrightarrow & -420x \color{red}{+56} \color{blue}{-56} \color{blue}{-72x} & = & \color{red}{72x} +9 \color{blue}{-72x} \color{blue}{-56} \\\Leftrightarrow & -420x-72x& = & 9-56 \\\Leftrightarrow & \color{red}{-492} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-492} & & \\\Leftrightarrow & x = \frac{47}{492} & & \\ & V = \left\{ \frac{47}{492} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 4x+\frac{8}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{231x} +88 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-24} \\\Leftrightarrow & 132x-231x& = & 88-24 \\\Leftrightarrow & \color{red}{-99} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-99} & & \\\Leftrightarrow & x = \frac{-64}{99} & & \\ & V = \left\{ \frac{-64}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{4})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -21x-\frac{35}{4}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-420}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -420x \color{red}{-175} & = & \color{red}{160x} +18 \\\Leftrightarrow & -420x \color{red}{-175} \color{blue}{+175} \color{blue}{-160x} & = & \color{red}{160x} +18 \color{blue}{-160x} \color{blue}{+175} \\\Leftrightarrow & -420x-160x& = & 18+175 \\\Leftrightarrow & \color{red}{-580} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-580} & & \\\Leftrightarrow & x = \frac{-193}{580} & & \\ & V = \left\{ \frac{-193}{580} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{+16} & = & \color{red}{162x} +15 \\\Leftrightarrow & -72x \color{red}{+16} \color{blue}{-16} \color{blue}{-162x} & = & \color{red}{162x} +15 \color{blue}{-162x} \color{blue}{-16} \\\Leftrightarrow & -72x-162x& = & 15-16 \\\Leftrightarrow & \color{red}{-234} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-234} & & \\\Leftrightarrow & x = \frac{1}{234} & & \\ & V = \left\{ \frac{1}{234} \right\} & \\\end{align}\)