Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{14}{5}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{280x} +30 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{-280x} & = & \color{red}{280x} +30 \color{blue}{-280x} \color{blue}{-98} \\\Leftrightarrow & 735x-280x& = & 30-98 \\\Leftrightarrow & \color{red}{455} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{455} & & \\ & V = \left\{ \frac{-68}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{6}{5}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-6} & = & \color{red}{-45x} +8 \\\Leftrightarrow & -40x \color{red}{-6} \color{blue}{+6} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{+6} \\\Leftrightarrow & -40x+45x& = & 8+6 \\\Leftrightarrow & \color{red}{5} x& = & 14 \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{11})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -35x+\frac{14}{11}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1540}{ \color{blue}{44} }x+ \frac{56}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1540x \color{red}{+56} & = & \color{red}{396x} +99 \\\Leftrightarrow & -1540x \color{red}{+56} \color{blue}{-56} \color{blue}{-396x} & = & \color{red}{396x} +99 \color{blue}{-396x} \color{blue}{-56} \\\Leftrightarrow & -1540x-396x& = & 99-56 \\\Leftrightarrow & \color{red}{-1936} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-1936} & & \\\Leftrightarrow & x = \frac{-43}{1936} & & \\ & V = \left\{ \frac{-43}{1936} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+72} & = & \color{red}{75x} +40 \\\Leftrightarrow & 270x \color{red}{+72} \color{blue}{-72} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-72} \\\Leftrightarrow & 270x-75x& = & 40-72 \\\Leftrightarrow & \color{red}{195} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{195} & & \\ & V = \left\{ \frac{-32}{195} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{-165x} +25 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{+132} \\\Leftrightarrow & 880x+165x& = & 25+132 \\\Leftrightarrow & \color{red}{1045} x& = & 157 \\\Leftrightarrow & x = \frac{157}{1045} & & \\ & V = \left\{ \frac{157}{1045} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-10} & = & \color{red}{49x} +6 \\\Leftrightarrow & 28x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & 28x-49x& = & 6+10 \\\Leftrightarrow & \color{red}{-21} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-21} & & \\\Leftrightarrow & x = \frac{-16}{21} & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & 2x+\frac{9}{8} \\\Leftrightarrow & -25x-\frac{10}{7}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1400}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{112}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1400x \color{red}{-80} & = & \color{red}{112x} +63 \\\Leftrightarrow & -1400x \color{red}{-80} \color{blue}{+80} \color{blue}{-112x} & = & \color{red}{112x} +63 \color{blue}{-112x} \color{blue}{+80} \\\Leftrightarrow & -1400x-112x& = & 63+80 \\\Leftrightarrow & \color{red}{-1512} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1512} & & \\\Leftrightarrow & x = \frac{-143}{1512} & & \\ & V = \left\{ \frac{-143}{1512} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{2})& = & 6x+\frac{6}{7} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 6x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x- \frac{175}{ \color{blue}{14} })& = & (\frac{84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{-175} & = & \color{red}{84x} +12 \\\Leftrightarrow & 350x \color{red}{-175} \color{blue}{+175} \color{blue}{-84x} & = & \color{red}{84x} +12 \color{blue}{-84x} \color{blue}{+175} \\\Leftrightarrow & 350x-84x& = & 12+175 \\\Leftrightarrow & \color{red}{266} x& = & 187 \\\Leftrightarrow & x = \frac{187}{266} & & \\ & V = \left\{ \frac{187}{266} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & -4x+\frac{7}{5} \\\Leftrightarrow & 25x-\frac{25}{11}& = & -4x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{-125} & = & \color{red}{-220x} +77 \\\Leftrightarrow & 1375x \color{red}{-125} \color{blue}{+125} \color{blue}{+220x} & = & \color{red}{-220x} +77 \color{blue}{+220x} \color{blue}{+125} \\\Leftrightarrow & 1375x+220x& = & 77+125 \\\Leftrightarrow & \color{red}{1595} x& = & 202 \\\Leftrightarrow & x = \frac{202}{1595} & & \\ & V = \left\{ \frac{202}{1595} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+220} & = & \color{red}{-165x} +27 \\\Leftrightarrow & -396x \color{red}{+220} \color{blue}{-220} \color{blue}{+165x} & = & \color{red}{-165x} +27 \color{blue}{+165x} \color{blue}{-220} \\\Leftrightarrow & -396x+165x& = & 27-220 \\\Leftrightarrow & \color{red}{-231} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{-231} & & \\\Leftrightarrow & x = \frac{193}{231} & & \\ & V = \left\{ \frac{193}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-90} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -396x \color{red}{-90} \color{blue}{+90} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+90} \\\Leftrightarrow & -396x+165x& = & 44+90 \\\Leftrightarrow & \color{red}{-231} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-231} & & \\\Leftrightarrow & x = \frac{-134}{231} & & \\ & V = \left\{ \frac{-134}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{4})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -21x+\frac{21}{4}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{63}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+63} & = & \color{red}{-96x} +16 \\\Leftrightarrow & -252x \color{red}{+63} \color{blue}{-63} \color{blue}{+96x} & = & \color{red}{-96x} +16 \color{blue}{+96x} \color{blue}{-63} \\\Leftrightarrow & -252x+96x& = & 16-63 \\\Leftrightarrow & \color{red}{-156} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-156} & & \\\Leftrightarrow & x = \frac{47}{156} & & \\ & V = \left\{ \frac{47}{156} \right\} & \\\end{align}\)