Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-900}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -900x \color{red}{+80} & = & \color{red}{630x} +81 \\\Leftrightarrow & -900x \color{red}{+80} \color{blue}{-80} \color{blue}{-630x} & = & \color{red}{630x} +81 \color{blue}{-630x} \color{blue}{-80} \\\Leftrightarrow & -900x-630x& = & 81-80 \\\Leftrightarrow & \color{red}{-1530} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-1530} & & \\\Leftrightarrow & x = \frac{-1}{1530} & & \\ & V = \left\{ \frac{-1}{1530} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{+54} & = & \color{red}{264x} +22 \\\Leftrightarrow & -594x \color{red}{+54} \color{blue}{-54} \color{blue}{-264x} & = & \color{red}{264x} +22 \color{blue}{-264x} \color{blue}{-54} \\\Leftrightarrow & -594x-264x& = & 22-54 \\\Leftrightarrow & \color{red}{-858} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-858} & & \\\Leftrightarrow & x = \frac{16}{429} & & \\ & V = \left\{ \frac{16}{429} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{11})& = & 8x+\frac{7}{4} \\\Leftrightarrow & -21x-\frac{21}{11}& = & 8x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-924}{ \color{blue}{44} }x- \frac{84}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{352x} +77 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{-352x} & = & \color{red}{352x} +77 \color{blue}{-352x} \color{blue}{+84} \\\Leftrightarrow & -924x-352x& = & 77+84 \\\Leftrightarrow & \color{red}{-1276} x& = & 161 \\\Leftrightarrow & x = \frac{161}{-1276} & & \\\Leftrightarrow & x = \frac{-161}{1276} & & \\ & V = \left\{ \frac{-161}{1276} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+90} & = & \color{red}{105x} +28 \\\Leftrightarrow & 504x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 504x-105x& = & 28-90 \\\Leftrightarrow & \color{red}{399} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{399} & & \\ & V = \left\{ \frac{-62}{399} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -10x-\frac{8}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-24} & = & \color{red}{147x} +35 \\\Leftrightarrow & -210x \color{red}{-24} \color{blue}{+24} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+24} \\\Leftrightarrow & -210x-147x& = & 35+24 \\\Leftrightarrow & \color{red}{-357} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-357} & & \\\Leftrightarrow & x = \frac{-59}{357} & & \\ & V = \left\{ \frac{-59}{357} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+60} & = & \color{red}{27x} +8 \\\Leftrightarrow & 90x \color{red}{+60} \color{blue}{-60} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-60} \\\Leftrightarrow & 90x-27x& = & 8-60 \\\Leftrightarrow & \color{red}{63} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{63} & & \\ & V = \left\{ \frac{-52}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & 350x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{595} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{595} & & \\ & V = \left\{ \frac{-8}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{4})& = & -4x+\frac{8}{11} \\\Leftrightarrow & -15x-\frac{9}{4}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{99}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-99} & = & \color{red}{-176x} +32 \\\Leftrightarrow & -660x \color{red}{-99} \color{blue}{+99} \color{blue}{+176x} & = & \color{red}{-176x} +32 \color{blue}{+176x} \color{blue}{+99} \\\Leftrightarrow & -660x+176x& = & 32+99 \\\Leftrightarrow & \color{red}{-484} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-484} & & \\\Leftrightarrow & x = \frac{-131}{484} & & \\ & V = \left\{ \frac{-131}{484} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{6}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+6} & = & \color{red}{25x} +4 \\\Leftrightarrow & -60x \color{red}{+6} \color{blue}{-6} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-6} \\\Leftrightarrow & -60x-25x& = & 4-6 \\\Leftrightarrow & \color{red}{-85} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-85} & & \\\Leftrightarrow & x = \frac{2}{85} & & \\ & V = \left\{ \frac{2}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{245x} +42 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-50} \\\Leftrightarrow & -350x-245x& = & 42-50 \\\Leftrightarrow & \color{red}{-595} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-595} & & \\\Leftrightarrow & x = \frac{8}{595} & & \\ & V = \left\{ \frac{8}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{50x} +45 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 60x-50x& = & 45-12 \\\Leftrightarrow & \color{red}{10} x& = & 33 \\\Leftrightarrow & x = \frac{33}{10} & & \\ & V = \left\{ \frac{33}{10} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+10} & = & \color{red}{21x} +9 \\\Leftrightarrow & -140x \color{red}{+10} \color{blue}{-10} \color{blue}{-21x} & = & \color{red}{21x} +9 \color{blue}{-21x} \color{blue}{-10} \\\Leftrightarrow & -140x-21x& = & 9-10 \\\Leftrightarrow & \color{red}{-161} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-161} & & \\\Leftrightarrow & x = \frac{1}{161} & & \\ & V = \left\{ \frac{1}{161} \right\} & \\\end{align}\)