Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{-245x} +56 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & 1050x+245x& = & 56+150 \\\Leftrightarrow & \color{red}{1295} x& = & 206 \\\Leftrightarrow & x = \frac{206}{1295} & & \\ & V = \left\{ \frac{206}{1295} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{-175x} +14 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & -420x+175x& = & 14-150 \\\Leftrightarrow & \color{red}{-245} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-245} & & \\\Leftrightarrow & x = \frac{136}{245} & & \\ & V = \left\{ \frac{136}{245} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{+60} & = & \color{red}{490x} +63 \\\Leftrightarrow & 700x \color{red}{+60} \color{blue}{-60} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-60} \\\Leftrightarrow & 700x-490x& = & 63-60 \\\Leftrightarrow & \color{red}{210} x& = & 3 \\\Leftrightarrow & x = \frac{3}{210} & & \\\Leftrightarrow & x = \frac{1}{70} & & \\ & V = \left\{ \frac{1}{70} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{15}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-45} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & -252x+105x& = & 56+45 \\\Leftrightarrow & \color{red}{-147} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-147} & & \\\Leftrightarrow & x = \frac{-101}{147} & & \\ & V = \left\{ \frac{-101}{147} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{8}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+56} & = & \color{red}{175x} +45 \\\Leftrightarrow & 280x \color{red}{+56} \color{blue}{-56} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-56} \\\Leftrightarrow & 280x-175x& = & 45-56 \\\Leftrightarrow & \color{red}{105} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{105} & & \\ & V = \left\{ \frac{-11}{105} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-18} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -252x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & -252x+105x& = & 28+18 \\\Leftrightarrow & \color{red}{-147} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-147} & & \\\Leftrightarrow & x = \frac{-46}{147} & & \\ & V = \left\{ \frac{-46}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{5})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{+4} & = & \color{red}{45x} +2 \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{-45x} & = & \color{red}{45x} +2 \color{blue}{-45x} \color{blue}{-4} \\\Leftrightarrow & -20x-45x& = & 2-4 \\\Leftrightarrow & \color{red}{-65} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-65} & & \\\Leftrightarrow & x = \frac{2}{65} & & \\ & V = \left\{ \frac{2}{65} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & 4x+\frac{4}{5} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{+75} & = & \color{red}{160x} +32 \\\Leftrightarrow & 360x \color{red}{+75} \color{blue}{-75} \color{blue}{-160x} & = & \color{red}{160x} +32 \color{blue}{-160x} \color{blue}{-75} \\\Leftrightarrow & 360x-160x& = & 32-75 \\\Leftrightarrow & \color{red}{200} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{200} & & \\ & V = \left\{ \frac{-43}{200} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{1}{3})& = & 3x+\frac{7}{10} \\\Leftrightarrow & -35x+\frac{7}{3}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{+70} & = & \color{red}{90x} +21 \\\Leftrightarrow & -1050x \color{red}{+70} \color{blue}{-70} \color{blue}{-90x} & = & \color{red}{90x} +21 \color{blue}{-90x} \color{blue}{-70} \\\Leftrightarrow & -1050x-90x& = & 21-70 \\\Leftrightarrow & \color{red}{-1140} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-1140} & & \\\Leftrightarrow & x = \frac{49}{1140} & & \\ & V = \left\{ \frac{49}{1140} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{147x} +70 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & 126x-147x& = & 70-18 \\\Leftrightarrow & \color{red}{-21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-21} & & \\\Leftrightarrow & x = \frac{-52}{21} & & \\ & V = \left\{ \frac{-52}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{9})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 6x-\frac{10}{9}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x- \frac{40}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{-40} & = & \color{red}{-180x} +15 \\\Leftrightarrow & 216x \color{red}{-40} \color{blue}{+40} \color{blue}{+180x} & = & \color{red}{-180x} +15 \color{blue}{+180x} \color{blue}{+40} \\\Leftrightarrow & 216x+180x& = & 15+40 \\\Leftrightarrow & \color{red}{396} x& = & 55 \\\Leftrightarrow & x = \frac{55}{396} & & \\\Leftrightarrow & x = \frac{5}{36} & & \\ & V = \left\{ \frac{5}{36} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{8}{9}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1080}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1080x \color{red}{-80} & = & \color{red}{450x} +63 \\\Leftrightarrow & -1080x \color{red}{-80} \color{blue}{+80} \color{blue}{-450x} & = & \color{red}{450x} +63 \color{blue}{-450x} \color{blue}{+80} \\\Leftrightarrow & -1080x-450x& = & 63+80 \\\Leftrightarrow & \color{red}{-1530} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1530} & & \\\Leftrightarrow & x = \frac{-143}{1530} & & \\ & V = \left\{ \frac{-143}{1530} \right\} & \\\end{align}\)