Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{63x} +56 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 420x-63x& = & 56-30 \\\Leftrightarrow & \color{red}{357} x& = & 26 \\\Leftrightarrow & x = \frac{26}{357} & & \\ & V = \left\{ \frac{26}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{231x} +18 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 660x-231x& = & 18-220 \\\Leftrightarrow & \color{red}{429} x& = & -202 \\\Leftrightarrow & x = \frac{-202}{429} & & \\ & V = \left\{ \frac{-202}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{30}{11}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+150} & = & \color{red}{275x} +33 \\\Leftrightarrow & 660x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +33 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & 660x-275x& = & 33-150 \\\Leftrightarrow & \color{red}{385} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{385} & & \\ & V = \left\{ \frac{-117}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{245x} +45 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{-42} \\\Leftrightarrow & -210x-245x& = & 45-42 \\\Leftrightarrow & \color{red}{-455} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-455} & & \\\Leftrightarrow & x = \frac{-3}{455} & & \\ & V = \left\{ \frac{-3}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{11})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -18x+\frac{24}{11}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{+24} & = & \color{red}{-99x} +10 \\\Leftrightarrow & -198x \color{red}{+24} \color{blue}{-24} \color{blue}{+99x} & = & \color{red}{-99x} +10 \color{blue}{+99x} \color{blue}{-24} \\\Leftrightarrow & -198x+99x& = & 10-24 \\\Leftrightarrow & \color{red}{-99} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-99} & & \\\Leftrightarrow & x = \frac{14}{99} & & \\ & V = \left\{ \frac{14}{99} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{+12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -100x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -100x+35x& = & 8-12 \\\Leftrightarrow & \color{red}{-65} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-65} & & \\\Leftrightarrow & x = \frac{4}{65} & & \\ & V = \left\{ \frac{4}{65} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{-27x} +30 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{+27x} & = & \color{red}{-27x} +30 \color{blue}{+27x} \color{blue}{+28} \\\Leftrightarrow & -126x+27x& = & 30+28 \\\Leftrightarrow & \color{red}{-99} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-99} & & \\\Leftrightarrow & x = \frac{-58}{99} & & \\ & V = \left\{ \frac{-58}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 10+132 \\\Leftrightarrow & \color{red}{-385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-385} & & \\\Leftrightarrow & x = \frac{-142}{385} & & \\ & V = \left\{ \frac{-142}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-81} & = & \color{red}{225x} +25 \\\Leftrightarrow & 270x \color{red}{-81} \color{blue}{+81} \color{blue}{-225x} & = & \color{red}{225x} +25 \color{blue}{-225x} \color{blue}{+81} \\\Leftrightarrow & 270x-225x& = & 25+81 \\\Leftrightarrow & \color{red}{45} x& = & 106 \\\Leftrightarrow & x = \frac{106}{45} & & \\ & V = \left\{ \frac{106}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{8}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-24} \\\Leftrightarrow & -120x+135x& = & 40-24 \\\Leftrightarrow & \color{red}{15} x& = & 16 \\\Leftrightarrow & x = \frac{16}{15} & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{-36} & = & \color{red}{-110x} +77 \\\Leftrightarrow & 396x \color{red}{-36} \color{blue}{+36} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{+36} \\\Leftrightarrow & 396x+110x& = & 77+36 \\\Leftrightarrow & \color{red}{506} x& = & 113 \\\Leftrightarrow & x = \frac{113}{506} & & \\ & V = \left\{ \frac{113}{506} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{99x} +110 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{-99x} & = & \color{red}{99x} +110 \color{blue}{-99x} \color{blue}{+30} \\\Leftrightarrow & 660x-99x& = & 110+30 \\\Leftrightarrow & \color{red}{561} x& = & 140 \\\Leftrightarrow & x = \frac{140}{561} & & \\ & V = \left\{ \frac{140}{561} \right\} & \\\end{align}\)