Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{-60} \\\Leftrightarrow & 660x+297x& = & 22-60 \\\Leftrightarrow & \color{red}{957} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{957} & & \\ & V = \left\{ \frac{-38}{957} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x- \frac{128}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{-128} & = & \color{red}{-168x} +49 \\\Leftrightarrow & 448x \color{red}{-128} \color{blue}{+128} \color{blue}{+168x} & = & \color{red}{-168x} +49 \color{blue}{+168x} \color{blue}{+128} \\\Leftrightarrow & 448x+168x& = & 49+128 \\\Leftrightarrow & \color{red}{616} x& = & 177 \\\Leftrightarrow & x = \frac{177}{616} & & \\ & V = \left\{ \frac{177}{616} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-88} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -594x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -594x+693x& = & 45+88 \\\Leftrightarrow & \color{red}{99} x& = & 133 \\\Leftrightarrow & x = \frac{133}{99} & & \\ & V = \left\{ \frac{133}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{5})& = & 3x+\frac{8}{5} \\\Leftrightarrow & 28x-\frac{21}{5}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{140}{ \color{blue}{5} }x- \frac{21}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 140x \color{red}{-21} & = & \color{red}{15x} +8 \\\Leftrightarrow & 140x \color{red}{-21} \color{blue}{+21} \color{blue}{-15x} & = & \color{red}{15x} +8 \color{blue}{-15x} \color{blue}{+21} \\\Leftrightarrow & 140x-15x& = & 8+21 \\\Leftrightarrow & \color{red}{125} x& = & 29 \\\Leftrightarrow & x = \frac{29}{125} & & \\ & V = \left\{ \frac{29}{125} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1540}{ \color{blue}{110} }x- \frac{210}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1540x \color{red}{-210} & = & \color{red}{-330x} +99 \\\Leftrightarrow & -1540x \color{red}{-210} \color{blue}{+210} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{+210} \\\Leftrightarrow & -1540x+330x& = & 99+210 \\\Leftrightarrow & \color{red}{-1210} x& = & 309 \\\Leftrightarrow & x = \frac{309}{-1210} & & \\\Leftrightarrow & x = \frac{-309}{1210} & & \\ & V = \left\{ \frac{-309}{1210} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{11})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -28x-\frac{28}{11}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-84} & = & \color{red}{297x} +110 \\\Leftrightarrow & -924x \color{red}{-84} \color{blue}{+84} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{+84} \\\Leftrightarrow & -924x-297x& = & 110+84 \\\Leftrightarrow & \color{red}{-1221} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1221} & & \\\Leftrightarrow & x = \frac{-194}{1221} & & \\ & V = \left\{ \frac{-194}{1221} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{8})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -9x+\frac{15}{8}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-216}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -216x \color{red}{+45} & = & \color{red}{120x} +16 \\\Leftrightarrow & -216x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +16 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & -216x-120x& = & 16-45 \\\Leftrightarrow & \color{red}{-336} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-336} & & \\\Leftrightarrow & x = \frac{29}{336} & & \\ & V = \left\{ \frac{29}{336} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-220} & = & \color{red}{-264x} +6 \\\Leftrightarrow & -495x \color{red}{-220} \color{blue}{+220} \color{blue}{+264x} & = & \color{red}{-264x} +6 \color{blue}{+264x} \color{blue}{+220} \\\Leftrightarrow & -495x+264x& = & 6+220 \\\Leftrightarrow & \color{red}{-231} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-231} & & \\\Leftrightarrow & x = \frac{-226}{231} & & \\ & V = \left\{ \frac{-226}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{-30} & = & \color{red}{77x} +5 \\\Leftrightarrow & 264x \color{red}{-30} \color{blue}{+30} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+30} \\\Leftrightarrow & 264x-77x& = & 5+30 \\\Leftrightarrow & \color{red}{187} x& = & 35 \\\Leftrightarrow & x = \frac{35}{187} & & \\ & V = \left\{ \frac{35}{187} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{-225x} +35 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{+54} \\\Leftrightarrow & 270x+225x& = & 35+54 \\\Leftrightarrow & \color{red}{495} x& = & 89 \\\Leftrightarrow & x = \frac{89}{495} & & \\ & V = \left\{ \frac{89}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{-36} \\\Leftrightarrow & -120x+135x& = & 50-36 \\\Leftrightarrow & \color{red}{15} x& = & 14 \\\Leftrightarrow & x = \frac{14}{15} & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{4})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{25}{4}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+175} & = & \color{red}{-252x} +40 \\\Leftrightarrow & 560x \color{red}{+175} \color{blue}{-175} \color{blue}{+252x} & = & \color{red}{-252x} +40 \color{blue}{+252x} \color{blue}{-175} \\\Leftrightarrow & 560x+252x& = & 40-175 \\\Leftrightarrow & \color{red}{812} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{812} & & \\ & V = \left\{ \frac{-135}{812} \right\} & \\\end{align}\)