Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{8}{5}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{-30x} +45 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +45 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & -80x+30x& = & 45+16 \\\Leftrightarrow & \color{red}{-50} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-50} & & \\\Leftrightarrow & x = \frac{-61}{50} & & \\ & V = \left\{ \frac{-61}{50} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-270} & = & \color{red}{315x} +70 \\\Leftrightarrow & -756x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & -756x-315x& = & 70+270 \\\Leftrightarrow & \color{red}{-1071} x& = & 340 \\\Leftrightarrow & x = \frac{340}{-1071} & & \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-110} & = & \color{red}{-231x} +28 \\\Leftrightarrow & -1540x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -1540x+231x& = & 28+110 \\\Leftrightarrow & \color{red}{-1309} x& = & 138 \\\Leftrightarrow & x = \frac{138}{-1309} & & \\\Leftrightarrow & x = \frac{-138}{1309} & & \\ & V = \left\{ \frac{-138}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -990x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -990x+275x& = & 30-132 \\\Leftrightarrow & \color{red}{-715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-715} & & \\\Leftrightarrow & x = \frac{102}{715} & & \\ & V = \left\{ \frac{102}{715} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{165x} +44 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -396x-165x& = & 44+54 \\\Leftrightarrow & \color{red}{-561} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-561} & & \\\Leftrightarrow & x = \frac{-98}{561} & & \\ & V = \left\{ \frac{-98}{561} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{9}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+99} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 462x \color{red}{+99} \color{blue}{-99} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-99} \\\Leftrightarrow & 462x+385x& = & 42-99 \\\Leftrightarrow & \color{red}{847} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{847} & & \\ & V = \left\{ \frac{-57}{847} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{8})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 20x-\frac{25}{8}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-175} & = & \color{red}{-504x} +24 \\\Leftrightarrow & 1120x \color{red}{-175} \color{blue}{+175} \color{blue}{+504x} & = & \color{red}{-504x} +24 \color{blue}{+504x} \color{blue}{+175} \\\Leftrightarrow & 1120x+504x& = & 24+175 \\\Leftrightarrow & \color{red}{1624} x& = & 199 \\\Leftrightarrow & x = \frac{199}{1624} & & \\ & V = \left\{ \frac{199}{1624} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+42} & = & \color{red}{-18x} +10 \\\Leftrightarrow & 189x \color{red}{+42} \color{blue}{-42} \color{blue}{+18x} & = & \color{red}{-18x} +10 \color{blue}{+18x} \color{blue}{-42} \\\Leftrightarrow & 189x+18x& = & 10-42 \\\Leftrightarrow & \color{red}{207} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{207} & & \\ & V = \left\{ \frac{-32}{207} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-10} & = & \color{red}{-33x} +10 \\\Leftrightarrow & 110x \color{red}{-10} \color{blue}{+10} \color{blue}{+33x} & = & \color{red}{-33x} +10 \color{blue}{+33x} \color{blue}{+10} \\\Leftrightarrow & 110x+33x& = & 10+10 \\\Leftrightarrow & \color{red}{143} x& = & 20 \\\Leftrightarrow & x = \frac{20}{143} & & \\ & V = \left\{ \frac{20}{143} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-165} & = & \color{red}{132x} +32 \\\Leftrightarrow & 1100x \color{red}{-165} \color{blue}{+165} \color{blue}{-132x} & = & \color{red}{132x} +32 \color{blue}{-132x} \color{blue}{+165} \\\Leftrightarrow & 1100x-132x& = & 32+165 \\\Leftrightarrow & \color{red}{968} x& = & 197 \\\Leftrightarrow & x = \frac{197}{968} & & \\ & V = \left\{ \frac{197}{968} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{2})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 10x+\frac{25}{2}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+225} & = & \color{red}{162x} +4 \\\Leftrightarrow & 180x \color{red}{+225} \color{blue}{-225} \color{blue}{-162x} & = & \color{red}{162x} +4 \color{blue}{-162x} \color{blue}{-225} \\\Leftrightarrow & 180x-162x& = & 4-225 \\\Leftrightarrow & \color{red}{18} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{18} & & \\ & V = \left\{ \frac{-221}{18} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{11})& = & 2x+\frac{5}{8} \\\Leftrightarrow & 21x-\frac{28}{11}& = & 2x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x- \frac{224}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{-224} & = & \color{red}{176x} +55 \\\Leftrightarrow & 1848x \color{red}{-224} \color{blue}{+224} \color{blue}{-176x} & = & \color{red}{176x} +55 \color{blue}{-176x} \color{blue}{+224} \\\Leftrightarrow & 1848x-176x& = & 55+224 \\\Leftrightarrow & \color{red}{1672} x& = & 279 \\\Leftrightarrow & x = \frac{279}{1672} & & \\ & V = \left\{ \frac{279}{1672} \right\} & \\\end{align}\)