Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-420}{ \color{blue}{14} }x+ \frac{48}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -420x \color{red}{+48} & = & \color{red}{-98x} +49 \\\Leftrightarrow & -420x \color{red}{+48} \color{blue}{-48} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{-48} \\\Leftrightarrow & -420x+98x& = & 49-48 \\\Leftrightarrow & \color{red}{-322} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-322} & & \\\Leftrightarrow & x = \frac{-1}{322} & & \\ & V = \left\{ \frac{-1}{322} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{2})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 20x+\frac{15}{2}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+165} & = & \color{red}{-66x} +10 \\\Leftrightarrow & 440x \color{red}{+165} \color{blue}{-165} \color{blue}{+66x} & = & \color{red}{-66x} +10 \color{blue}{+66x} \color{blue}{-165} \\\Leftrightarrow & 440x+66x& = & 10-165 \\\Leftrightarrow & \color{red}{506} x& = & -155 \\\Leftrightarrow & x = \frac{-155}{506} & & \\ & V = \left\{ \frac{-155}{506} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 4x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 4x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1260}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} })& = & (\frac{336}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1260x \color{red}{+72} & = & \color{red}{336x} +49 \\\Leftrightarrow & -1260x \color{red}{+72} \color{blue}{-72} \color{blue}{-336x} & = & \color{red}{336x} +49 \color{blue}{-336x} \color{blue}{-72} \\\Leftrightarrow & -1260x-336x& = & 49-72 \\\Leftrightarrow & \color{red}{-1596} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-1596} & & \\\Leftrightarrow & x = \frac{23}{1596} & & \\ & V = \left\{ \frac{23}{1596} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{9})& = & -8x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{20}{9}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{+40} & = & \color{red}{-144x} +15 \\\Leftrightarrow & -270x \color{red}{+40} \color{blue}{-40} \color{blue}{+144x} & = & \color{red}{-144x} +15 \color{blue}{+144x} \color{blue}{-40} \\\Leftrightarrow & -270x+144x& = & 15-40 \\\Leftrightarrow & \color{red}{-126} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-126} & & \\\Leftrightarrow & x = \frac{25}{126} & & \\ & V = \left\{ \frac{25}{126} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{9})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 10x+\frac{20}{9}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+40} & = & \color{red}{-126x} +21 \\\Leftrightarrow & 180x \color{red}{+40} \color{blue}{-40} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-40} \\\Leftrightarrow & 180x+126x& = & 21-40 \\\Leftrightarrow & \color{red}{306} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{306} & & \\ & V = \left\{ \frac{-19}{306} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-40} & = & \color{red}{-12x} +27 \\\Leftrightarrow & 90x \color{red}{-40} \color{blue}{+40} \color{blue}{+12x} & = & \color{red}{-12x} +27 \color{blue}{+12x} \color{blue}{+40} \\\Leftrightarrow & 90x+12x& = & 27+40 \\\Leftrightarrow & \color{red}{102} x& = & 67 \\\Leftrightarrow & x = \frac{67}{102} & & \\ & V = \left\{ \frac{67}{102} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{+216} & = & \color{red}{495x} +77 \\\Leftrightarrow & 1782x \color{red}{+216} \color{blue}{-216} \color{blue}{-495x} & = & \color{red}{495x} +77 \color{blue}{-495x} \color{blue}{-216} \\\Leftrightarrow & 1782x-495x& = & 77-216 \\\Leftrightarrow & \color{red}{1287} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{1287} & & \\ & V = \left\{ \frac{-139}{1287} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{6}{5}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-66} & = & \color{red}{-110x} +30 \\\Leftrightarrow & 825x \color{red}{-66} \color{blue}{+66} \color{blue}{+110x} & = & \color{red}{-110x} +30 \color{blue}{+110x} \color{blue}{+66} \\\Leftrightarrow & 825x+110x& = & 30+66 \\\Leftrightarrow & \color{red}{935} x& = & 96 \\\Leftrightarrow & x = \frac{96}{935} & & \\ & V = \left\{ \frac{96}{935} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{8})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{35}{8}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x+ \frac{385}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{+385} & = & \color{red}{-352x} +48 \\\Leftrightarrow & 3080x \color{red}{+385} \color{blue}{-385} \color{blue}{+352x} & = & \color{red}{-352x} +48 \color{blue}{+352x} \color{blue}{-385} \\\Leftrightarrow & 3080x+352x& = & 48-385 \\\Leftrightarrow & \color{red}{3432} x& = & -337 \\\Leftrightarrow & x = \frac{-337}{3432} & & \\ & V = \left\{ \frac{-337}{3432} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+54} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 945x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & 945x+441x& = & 14-54 \\\Leftrightarrow & \color{red}{1386} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{1386} & & \\\Leftrightarrow & x = \frac{-20}{693} & & \\ & V = \left\{ \frac{-20}{693} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -24x+\frac{24}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+264} & = & \color{red}{385x} +42 \\\Leftrightarrow & -1848x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & -1848x-385x& = & 42-264 \\\Leftrightarrow & \color{red}{-2233} x& = & -222 \\\Leftrightarrow & x = \frac{-222}{-2233} & & \\\Leftrightarrow & x = \frac{222}{2233} & & \\ & V = \left\{ \frac{222}{2233} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 28+18 \\\Leftrightarrow & \color{red}{21} x& = & 46 \\\Leftrightarrow & x = \frac{46}{21} & & \\ & V = \left\{ \frac{46}{21} \right\} & \\\end{align}\)