Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -70x+49x& = & 4+10 \\\Leftrightarrow & \color{red}{-21} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-21} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +15 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 15-24 \\\Leftrightarrow & \color{red}{70} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{70} & & \\ & V = \left\{ \frac{-9}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-108} & = & \color{red}{-225x} +35 \\\Leftrightarrow & -405x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & -405x+225x& = & 35+108 \\\Leftrightarrow & \color{red}{-180} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-180} & & \\\Leftrightarrow & x = \frac{-143}{180} & & \\ & V = \left\{ \frac{-143}{180} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{8})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{9}{8}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} })& = & (\frac{-160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{+45} & = & \color{red}{-160x} +48 \\\Leftrightarrow & -600x \color{red}{+45} \color{blue}{-45} \color{blue}{+160x} & = & \color{red}{-160x} +48 \color{blue}{+160x} \color{blue}{-45} \\\Leftrightarrow & -600x+160x& = & 48-45 \\\Leftrightarrow & \color{red}{-440} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-440} & & \\\Leftrightarrow & x = \frac{-3}{440} & & \\ & V = \left\{ \frac{-3}{440} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{-24} & = & \color{red}{84x} +21 \\\Leftrightarrow & 112x \color{red}{-24} \color{blue}{+24} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{+24} \\\Leftrightarrow & 112x-84x& = & 21+24 \\\Leftrightarrow & \color{red}{28} x& = & 45 \\\Leftrightarrow & x = \frac{45}{28} & & \\ & V = \left\{ \frac{45}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{3})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{28}{3}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{24x} +4 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{-24x} & = & \color{red}{24x} +4 \color{blue}{-24x} \color{blue}{+28} \\\Leftrightarrow & -84x-24x& = & 4+28 \\\Leftrightarrow & \color{red}{-108} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-108} & & \\\Leftrightarrow & x = \frac{-8}{27} & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{4}{9})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 14x+\frac{28}{9}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1260}{ \color{blue}{90} }x+ \frac{280}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1260x \color{red}{+280} & = & \color{red}{-270x} +81 \\\Leftrightarrow & 1260x \color{red}{+280} \color{blue}{-280} \color{blue}{+270x} & = & \color{red}{-270x} +81 \color{blue}{+270x} \color{blue}{-280} \\\Leftrightarrow & 1260x+270x& = & 81-280 \\\Leftrightarrow & \color{red}{1530} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{1530} & & \\ & V = \left\{ \frac{-199}{1530} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{-18} & = & \color{red}{-55x} +4 \\\Leftrightarrow & 264x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 264x+55x& = & 4+18 \\\Leftrightarrow & \color{red}{319} x& = & 22 \\\Leftrightarrow & x = \frac{22}{319} & & \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{245x} +42 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & -210x-245x& = & 42+30 \\\Leftrightarrow & \color{red}{-455} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-455} & & \\\Leftrightarrow & x = \frac{-72}{455} & & \\ & V = \left\{ \frac{-72}{455} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 6x+\frac{10}{3}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+50} & = & \color{red}{-75x} +6 \\\Leftrightarrow & 90x \color{red}{+50} \color{blue}{-50} \color{blue}{+75x} & = & \color{red}{-75x} +6 \color{blue}{+75x} \color{blue}{-50} \\\Leftrightarrow & 90x+75x& = & 6-50 \\\Leftrightarrow & \color{red}{165} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{165} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -28x-\frac{14}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1848}{ \color{blue}{66} }x- \frac{84}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1848x \color{red}{-84} & = & \color{red}{-330x} +77 \\\Leftrightarrow & -1848x \color{red}{-84} \color{blue}{+84} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+84} \\\Leftrightarrow & -1848x+330x& = & 77+84 \\\Leftrightarrow & \color{red}{-1518} x& = & 161 \\\Leftrightarrow & x = \frac{161}{-1518} & & \\\Leftrightarrow & x = \frac{-7}{66} & & \\ & V = \left\{ \frac{-7}{66} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+12} & = & \color{red}{-98x} +63 \\\Leftrightarrow & 56x \color{red}{+12} \color{blue}{-12} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-12} \\\Leftrightarrow & 56x+98x& = & 63-12 \\\Leftrightarrow & \color{red}{154} x& = & 51 \\\Leftrightarrow & x = \frac{51}{154} & & \\ & V = \left\{ \frac{51}{154} \right\} & \\\end{align}\)