Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{28}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+84} \\\Leftrightarrow & 210x+75x& = & 50+84 \\\Leftrightarrow & \color{red}{285} x& = & 134 \\\Leftrightarrow & x = \frac{134}{285} & & \\ & V = \left\{ \frac{134}{285} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{2})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{15}{2}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{90}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-90} & = & \color{red}{36x} +7 \\\Leftrightarrow & -240x \color{red}{-90} \color{blue}{+90} \color{blue}{-36x} & = & \color{red}{36x} +7 \color{blue}{-36x} \color{blue}{+90} \\\Leftrightarrow & -240x-36x& = & 7+90 \\\Leftrightarrow & \color{red}{-276} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-276} & & \\\Leftrightarrow & x = \frac{-97}{276} & & \\ & V = \left\{ \frac{-97}{276} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+18} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 180x \color{red}{+18} \color{blue}{-18} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-18} \\\Leftrightarrow & 180x+75x& = & 40-18 \\\Leftrightarrow & \color{red}{255} x& = & 22 \\\Leftrightarrow & x = \frac{22}{255} & & \\ & V = \left\{ \frac{22}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{9})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 28x-\frac{35}{9}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{-175} & = & \color{red}{-135x} +18 \\\Leftrightarrow & 1260x \color{red}{-175} \color{blue}{+175} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{+175} \\\Leftrightarrow & 1260x+135x& = & 18+175 \\\Leftrightarrow & \color{red}{1395} x& = & 193 \\\Leftrightarrow & x = \frac{193}{1395} & & \\ & V = \left\{ \frac{193}{1395} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{-28x} +10 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{+28x} & = & \color{red}{-28x} +10 \color{blue}{+28x} \color{blue}{+15} \\\Leftrightarrow & -24x+28x& = & 10+15 \\\Leftrightarrow & \color{red}{4} x& = & 25 \\\Leftrightarrow & x = \frac{25}{4} & & \\ & V = \left\{ \frac{25}{4} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & -720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & -720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{-1020} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1020} & & \\\Leftrightarrow & x = \frac{109}{1020} & & \\ & V = \left\{ \frac{109}{1020} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{315x} +10 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & 540x-315x& = & 10+108 \\\Leftrightarrow & \color{red}{225} x& = & 118 \\\Leftrightarrow & x = \frac{118}{225} & & \\ & V = \left\{ \frac{118}{225} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{16}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-16} & = & \color{red}{55x} +5 \\\Leftrightarrow & -132x \color{red}{-16} \color{blue}{+16} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+16} \\\Leftrightarrow & -132x-55x& = & 5+16 \\\Leftrightarrow & \color{red}{-187} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-187} & & \\\Leftrightarrow & x = \frac{-21}{187} & & \\ & V = \left\{ \frac{-21}{187} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x+\frac{8}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+8} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -84x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & -84x+35x& = & 9-8 \\\Leftrightarrow & \color{red}{-49} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-49} & & \\\Leftrightarrow & x = \frac{-1}{49} & & \\ & V = \left\{ \frac{-1}{49} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-720}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -720x \color{red}{-64} & = & \color{red}{504x} +63 \\\Leftrightarrow & -720x \color{red}{-64} \color{blue}{+64} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{+64} \\\Leftrightarrow & -720x-504x& = & 63+64 \\\Leftrightarrow & \color{red}{-1224} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-1224} & & \\\Leftrightarrow & x = \frac{-127}{1224} & & \\ & V = \left\{ \frac{-127}{1224} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 18x-\frac{12}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{-96} & = & \color{red}{440x} +77 \\\Leftrightarrow & 1584x \color{red}{-96} \color{blue}{+96} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{+96} \\\Leftrightarrow & 1584x-440x& = & 77+96 \\\Leftrightarrow & \color{red}{1144} x& = & 173 \\\Leftrightarrow & x = \frac{173}{1144} & & \\ & V = \left\{ \frac{173}{1144} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+108} & = & \color{red}{405x} +10 \\\Leftrightarrow & -360x \color{red}{+108} \color{blue}{-108} \color{blue}{-405x} & = & \color{red}{405x} +10 \color{blue}{-405x} \color{blue}{-108} \\\Leftrightarrow & -360x-405x& = & 10-108 \\\Leftrightarrow & \color{red}{-765} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-765} & & \\\Leftrightarrow & x = \frac{98}{765} & & \\ & V = \left\{ \frac{98}{765} \right\} & \\\end{align}\)