Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{30}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+30} & = & \color{red}{55x} +6 \\\Leftrightarrow & 132x \color{red}{+30} \color{blue}{-30} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-30} \\\Leftrightarrow & 132x-55x& = & 6-30 \\\Leftrightarrow & \color{red}{77} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{77} & & \\ & V = \left\{ \frac{-24}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{-275x} +88 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -660x+275x& = & 88+90 \\\Leftrightarrow & \color{red}{-385} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-385} & & \\\Leftrightarrow & x = \frac{-178}{385} & & \\ & V = \left\{ \frac{-178}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{4}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+20} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 120x \color{red}{+20} \color{blue}{-20} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{-20} \\\Leftrightarrow & 120x+45x& = & 18-20 \\\Leftrightarrow & \color{red}{165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 8x+\frac{16}{11}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+144} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 792x \color{red}{+144} \color{blue}{-144} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{-144} \\\Leftrightarrow & 792x+297x& = & 22-144 \\\Leftrightarrow & \color{red}{1089} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{1089} & & \\ & V = \left\{ \frac{-122}{1089} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{30}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+210} & = & \color{red}{385x} +110 \\\Leftrightarrow & 1848x \color{red}{+210} \color{blue}{-210} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-210} \\\Leftrightarrow & 1848x-385x& = & 110-210 \\\Leftrightarrow & \color{red}{1463} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{1463} & & \\ & V = \left\{ \frac{-100}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & -4x+\frac{5}{6} \\\Leftrightarrow & 9x+\frac{12}{11}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{594}{ \color{blue}{66} }x+ \frac{72}{ \color{blue}{66} })& = & (\frac{-264}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 594x \color{red}{+72} & = & \color{red}{-264x} +55 \\\Leftrightarrow & 594x \color{red}{+72} \color{blue}{-72} \color{blue}{+264x} & = & \color{red}{-264x} +55 \color{blue}{+264x} \color{blue}{-72} \\\Leftrightarrow & 594x+264x& = & 55-72 \\\Leftrightarrow & \color{red}{858} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{858} & & \\ & V = \left\{ \frac{-17}{858} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-90} \\\Leftrightarrow & 252x+105x& = & 56-90 \\\Leftrightarrow & \color{red}{357} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{357} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{10})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 12x-\frac{9}{10}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{40}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-99} & = & \color{red}{550x} +40 \\\Leftrightarrow & 1320x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +40 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & 1320x-550x& = & 40+99 \\\Leftrightarrow & \color{red}{770} x& = & 139 \\\Leftrightarrow & x = \frac{139}{770} & & \\ & V = \left\{ \frac{139}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-90} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -1260x \color{red}{-90} \color{blue}{+90} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{+90} \\\Leftrightarrow & -1260x+189x& = & 56+90 \\\Leftrightarrow & \color{red}{-1071} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-1071} & & \\\Leftrightarrow & x = \frac{-146}{1071} & & \\ & V = \left\{ \frac{-146}{1071} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+90} & = & \color{red}{-189x} +35 \\\Leftrightarrow & -504x \color{red}{+90} \color{blue}{-90} \color{blue}{+189x} & = & \color{red}{-189x} +35 \color{blue}{+189x} \color{blue}{-90} \\\Leftrightarrow & -504x+189x& = & 35-90 \\\Leftrightarrow & \color{red}{-315} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-315} & & \\\Leftrightarrow & x = \frac{11}{63} & & \\ & V = \left\{ \frac{11}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+108} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & 540x+225x& = & 50-108 \\\Leftrightarrow & \color{red}{765} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{765} & & \\ & V = \left\{ \frac{-58}{765} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-72} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 180x \color{red}{-72} \color{blue}{+72} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{+72} \\\Leftrightarrow & 180x+210x& = & 35+72 \\\Leftrightarrow & \color{red}{390} x& = & 107 \\\Leftrightarrow & x = \frac{107}{390} & & \\ & V = \left\{ \frac{107}{390} \right\} & \\\end{align}\)