Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{5})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 14x-\frac{28}{5}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{70}{ \color{blue}{5} }x- \frac{28}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 70x \color{red}{-28} & = & \color{red}{15x} +4 \\\Leftrightarrow & 70x \color{red}{-28} \color{blue}{+28} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+28} \\\Leftrightarrow & 70x-15x& = & 4+28 \\\Leftrightarrow & \color{red}{55} x& = & 32 \\\Leftrightarrow & x = \frac{32}{55} & & \\ & V = \left\{ \frac{32}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{+40} \\\Leftrightarrow & 120x+45x& = & 18+40 \\\Leftrightarrow & \color{red}{165} x& = & 58 \\\Leftrightarrow & x = \frac{58}{165} & & \\ & V = \left\{ \frac{58}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-28} \\\Leftrightarrow & -210x+245x& = & 10-28 \\\Leftrightarrow & \color{red}{35} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{35} & & \\ & V = \left\{ \frac{-18}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{9})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{720}{ \color{blue}{72} }x- \frac{32}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 720x \color{red}{-32} & = & \color{red}{504x} +27 \\\Leftrightarrow & 720x \color{red}{-32} \color{blue}{+32} \color{blue}{-504x} & = & \color{red}{504x} +27 \color{blue}{-504x} \color{blue}{+32} \\\Leftrightarrow & 720x-504x& = & 27+32 \\\Leftrightarrow & \color{red}{216} x& = & 59 \\\Leftrightarrow & x = \frac{59}{216} & & \\ & V = \left\{ \frac{59}{216} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{4})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+15} & = & \color{red}{28x} +9 \\\Leftrightarrow & 60x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +9 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & 60x-28x& = & 9-15 \\\Leftrightarrow & \color{red}{32} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{32} & & \\\Leftrightarrow & x = \frac{-3}{16} & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -3x+\frac{7}{6} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -3x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-528}{ \color{blue}{66} }x- \frac{96}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -528x \color{red}{-96} & = & \color{red}{-198x} +77 \\\Leftrightarrow & -528x \color{red}{-96} \color{blue}{+96} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{+96} \\\Leftrightarrow & -528x+198x& = & 77+96 \\\Leftrightarrow & \color{red}{-330} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-330} & & \\\Leftrightarrow & x = \frac{-173}{330} & & \\ & V = \left\{ \frac{-173}{330} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -24x+\frac{18}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-672}{ \color{blue}{28} }x+ \frac{72}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -672x \color{red}{+72} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -672x \color{red}{+72} \color{blue}{-72} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-72} \\\Leftrightarrow & -672x+140x& = & 63-72 \\\Leftrightarrow & \color{red}{-532} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-532} & & \\\Leftrightarrow & x = \frac{9}{532} & & \\ & V = \left\{ \frac{9}{532} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{12})& = & 6x+\frac{7}{2} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 6x+\frac{7}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{42}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+25} & = & \color{red}{72x} +42 \\\Leftrightarrow & -300x \color{red}{+25} \color{blue}{-25} \color{blue}{-72x} & = & \color{red}{72x} +42 \color{blue}{-72x} \color{blue}{-25} \\\Leftrightarrow & -300x-72x& = & 42-25 \\\Leftrightarrow & \color{red}{-372} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-372} & & \\\Leftrightarrow & x = \frac{-17}{372} & & \\ & V = \left\{ \frac{-17}{372} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+8} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 56x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & 56x+21x& = & 3-8 \\\Leftrightarrow & \color{red}{77} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{77} & & \\ & V = \left\{ \frac{-5}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{35}{3}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-70} & = & \color{red}{48x} +27 \\\Leftrightarrow & 126x \color{red}{-70} \color{blue}{+70} \color{blue}{-48x} & = & \color{red}{48x} +27 \color{blue}{-48x} \color{blue}{+70} \\\Leftrightarrow & 126x-48x& = & 27+70 \\\Leftrightarrow & \color{red}{78} x& = & 97 \\\Leftrightarrow & x = \frac{97}{78} & & \\ & V = \left\{ \frac{97}{78} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{240}{ \color{blue}{60} }x- \frac{72}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 240x \color{red}{-72} & = & \color{red}{180x} +35 \\\Leftrightarrow & 240x \color{red}{-72} \color{blue}{+72} \color{blue}{-180x} & = & \color{red}{180x} +35 \color{blue}{-180x} \color{blue}{+72} \\\Leftrightarrow & 240x-180x& = & 35+72 \\\Leftrightarrow & \color{red}{60} x& = & 107 \\\Leftrightarrow & x = \frac{107}{60} & & \\ & V = \left\{ \frac{107}{60} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -18x+\frac{24}{5}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+72} & = & \color{red}{60x} +20 \\\Leftrightarrow & -270x \color{red}{+72} \color{blue}{-72} \color{blue}{-60x} & = & \color{red}{60x} +20 \color{blue}{-60x} \color{blue}{-72} \\\Leftrightarrow & -270x-60x& = & 20-72 \\\Leftrightarrow & \color{red}{-330} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-330} & & \\\Leftrightarrow & x = \frac{26}{165} & & \\ & V = \left\{ \frac{26}{165} \right\} & \\\end{align}\)