Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-120} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{-120} \color{blue}{+120} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{+120} \\\Leftrightarrow & -660x-275x& = & 22+120 \\\Leftrightarrow & \color{red}{-935} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-935} & & \\\Leftrightarrow & x = \frac{-142}{935} & & \\ & V = \left\{ \frac{-142}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{16}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{48}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-48} & = & \color{red}{-135x} +40 \\\Leftrightarrow & 300x \color{red}{-48} \color{blue}{+48} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{+48} \\\Leftrightarrow & 300x+135x& = & 40+48 \\\Leftrightarrow & \color{red}{435} x& = & 88 \\\Leftrightarrow & x = \frac{88}{435} & & \\ & V = \left\{ \frac{88}{435} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{4})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -28x-\frac{35}{4}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-560}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -560x \color{red}{-175} & = & \color{red}{180x} +6 \\\Leftrightarrow & -560x \color{red}{-175} \color{blue}{+175} \color{blue}{-180x} & = & \color{red}{180x} +6 \color{blue}{-180x} \color{blue}{+175} \\\Leftrightarrow & -560x-180x& = & 6+175 \\\Leftrightarrow & \color{red}{-740} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-740} & & \\\Leftrightarrow & x = \frac{-181}{740} & & \\ & V = \left\{ \frac{-181}{740} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-840}{ \color{blue}{30} }x- \frac{280}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -840x \color{red}{-280} & = & \color{red}{270x} +27 \\\Leftrightarrow & -840x \color{red}{-280} \color{blue}{+280} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+280} \\\Leftrightarrow & -840x-270x& = & 27+280 \\\Leftrightarrow & \color{red}{-1110} x& = & 307 \\\Leftrightarrow & x = \frac{307}{-1110} & & \\\Leftrightarrow & x = \frac{-307}{1110} & & \\ & V = \left\{ \frac{-307}{1110} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+66} & = & \color{red}{693x} +70 \\\Leftrightarrow & -616x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +70 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & -616x-693x& = & 70-66 \\\Leftrightarrow & \color{red}{-1309} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-1309} & & \\\Leftrightarrow & x = \frac{-4}{1309} & & \\ & V = \left\{ \frac{-4}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{-15x} +5 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{+15x} & = & \color{red}{-15x} +5 \color{blue}{+15x} \color{blue}{-20} \\\Leftrightarrow & -36x+15x& = & 5-20 \\\Leftrightarrow & \color{red}{-21} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-21} & & \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{6})& = & -8x+\frac{7}{8} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -8x+\frac{7}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{140}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+140} & = & \color{red}{-192x} +21 \\\Leftrightarrow & -672x \color{red}{+140} \color{blue}{-140} \color{blue}{+192x} & = & \color{red}{-192x} +21 \color{blue}{+192x} \color{blue}{-140} \\\Leftrightarrow & -672x+192x& = & 21-140 \\\Leftrightarrow & \color{red}{-480} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-480} & & \\\Leftrightarrow & x = \frac{119}{480} & & \\ & V = \left\{ \frac{119}{480} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1344}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1344x \color{red}{+240} & = & \color{red}{280x} +63 \\\Leftrightarrow & -1344x \color{red}{+240} \color{blue}{-240} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{-240} \\\Leftrightarrow & -1344x-280x& = & 63-240 \\\Leftrightarrow & \color{red}{-1624} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{-1624} & & \\\Leftrightarrow & x = \frac{177}{1624} & & \\ & V = \left\{ \frac{177}{1624} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{4}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+44} & = & \color{red}{-495x} +54 \\\Leftrightarrow & 594x \color{red}{+44} \color{blue}{-44} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{-44} \\\Leftrightarrow & 594x+495x& = & 54-44 \\\Leftrightarrow & \color{red}{1089} x& = & 10 \\\Leftrightarrow & x = \frac{10}{1089} & & \\ & V = \left\{ \frac{10}{1089} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{11})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -35x+\frac{35}{11}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{+35} & = & \color{red}{-99x} +5 \\\Leftrightarrow & -385x \color{red}{+35} \color{blue}{-35} \color{blue}{+99x} & = & \color{red}{-99x} +5 \color{blue}{+99x} \color{blue}{-35} \\\Leftrightarrow & -385x+99x& = & 5-35 \\\Leftrightarrow & \color{red}{-286} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{-286} & & \\\Leftrightarrow & x = \frac{15}{143} & & \\ & V = \left\{ \frac{15}{143} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{6})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{25}{6}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x- \frac{75}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{-75} & = & \color{red}{-126x} +20 \\\Leftrightarrow & 270x \color{red}{-75} \color{blue}{+75} \color{blue}{+126x} & = & \color{red}{-126x} +20 \color{blue}{+126x} \color{blue}{+75} \\\Leftrightarrow & 270x+126x& = & 20+75 \\\Leftrightarrow & \color{red}{396} x& = & 95 \\\Leftrightarrow & x = \frac{95}{396} & & \\ & V = \left\{ \frac{95}{396} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-12} & = & \color{red}{25x} +3 \\\Leftrightarrow & 40x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +3 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 40x-25x& = & 3+12 \\\Leftrightarrow & \color{red}{15} x& = & 15 \\\Leftrightarrow & x = \frac{15}{15} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)