Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{2})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-40}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{14}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -40x \color{red}{-25} & = & \color{red}{14x} +3 \\\Leftrightarrow & -40x \color{red}{-25} \color{blue}{+25} \color{blue}{-14x} & = & \color{red}{14x} +3 \color{blue}{-14x} \color{blue}{+25} \\\Leftrightarrow & -40x-14x& = & 3+25 \\\Leftrightarrow & \color{red}{-54} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-54} & & \\\Leftrightarrow & x = \frac{-14}{27} & & \\ & V = \left\{ \frac{-14}{27} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & 3x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{-100} & = & \color{red}{330x} +33 \\\Leftrightarrow & -2200x \color{red}{-100} \color{blue}{+100} \color{blue}{-330x} & = & \color{red}{330x} +33 \color{blue}{-330x} \color{blue}{+100} \\\Leftrightarrow & -2200x-330x& = & 33+100 \\\Leftrightarrow & \color{red}{-2530} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-2530} & & \\\Leftrightarrow & x = \frac{-133}{2530} & & \\ & V = \left\{ \frac{-133}{2530} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{66x} +9 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{-66x} & = & \color{red}{66x} +9 \color{blue}{-66x} \color{blue}{-220} \\\Leftrightarrow & 495x-66x& = & 9-220 \\\Leftrightarrow & \color{red}{429} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{429} & & \\ & V = \left\{ \frac{-211}{429} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -405x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & -405x+225x& = & 10+108 \\\Leftrightarrow & \color{red}{-180} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-180} & & \\\Leftrightarrow & x = \frac{-59}{90} & & \\ & V = \left\{ \frac{-59}{90} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{4})& = & -4x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{25}{4}& = & -4x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x+ \frac{275}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{+275} & = & \color{red}{-176x} +20 \\\Leftrightarrow & 660x \color{red}{+275} \color{blue}{-275} \color{blue}{+176x} & = & \color{red}{-176x} +20 \color{blue}{+176x} \color{blue}{-275} \\\Leftrightarrow & 660x+176x& = & 20-275 \\\Leftrightarrow & \color{red}{836} x& = & -255 \\\Leftrightarrow & x = \frac{-255}{836} & & \\ & V = \left\{ \frac{-255}{836} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 360x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{435} x& = & 14 \\\Leftrightarrow & x = \frac{14}{435} & & \\ & V = \left\{ \frac{14}{435} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{35x} +10 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & -84x-35x& = & 10+30 \\\Leftrightarrow & \color{red}{-119} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-119} & & \\\Leftrightarrow & x = \frac{-40}{119} & & \\ & V = \left\{ \frac{-40}{119} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-98x} +49 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & -420x+98x& = & 49+60 \\\Leftrightarrow & \color{red}{-322} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-322} & & \\\Leftrightarrow & x = \frac{-109}{322} & & \\ & V = \left\{ \frac{-109}{322} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 10x-\frac{20}{7}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-20} & = & \color{red}{63x} +9 \\\Leftrightarrow & 70x \color{red}{-20} \color{blue}{+20} \color{blue}{-63x} & = & \color{red}{63x} +9 \color{blue}{-63x} \color{blue}{+20} \\\Leftrightarrow & 70x-63x& = & 9+20 \\\Leftrightarrow & \color{red}{7} x& = & 29 \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{+144} & = & \color{red}{616x} +77 \\\Leftrightarrow & 1584x \color{red}{+144} \color{blue}{-144} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{-144} \\\Leftrightarrow & 1584x-616x& = & 77-144 \\\Leftrightarrow & \color{red}{968} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{968} & & \\ & V = \left\{ \frac{-67}{968} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+84} & = & \color{red}{-539x} +44 \\\Leftrightarrow & 924x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +44 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & 924x+539x& = & 44-84 \\\Leftrightarrow & \color{red}{1463} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{1463} & & \\ & V = \left\{ \frac{-40}{1463} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{231x} +28 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{-66} \\\Leftrightarrow & 616x-231x& = & 28-66 \\\Leftrightarrow & \color{red}{385} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{385} & & \\ & V = \left\{ \frac{-38}{385} \right\} & \\\end{align}\)