Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-441x} +70 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & -378x+441x& = & 70-90 \\\Leftrightarrow & \color{red}{63} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-162} & = & \color{red}{225x} +20 \\\Leftrightarrow & 810x \color{red}{-162} \color{blue}{+162} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{+162} \\\Leftrightarrow & 810x-225x& = & 20+162 \\\Leftrightarrow & \color{red}{585} x& = & 182 \\\Leftrightarrow & x = \frac{182}{585} & & \\\Leftrightarrow & x = \frac{14}{45} & & \\ & V = \left\{ \frac{14}{45} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -5x+\frac{7}{12} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{+56} & = & \color{red}{-60x} +7 \\\Leftrightarrow & -336x \color{red}{+56} \color{blue}{-56} \color{blue}{+60x} & = & \color{red}{-60x} +7 \color{blue}{+60x} \color{blue}{-56} \\\Leftrightarrow & -336x+60x& = & 7-56 \\\Leftrightarrow & \color{red}{-276} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-276} & & \\\Leftrightarrow & x = \frac{49}{276} & & \\ & V = \left\{ \frac{49}{276} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+84} & = & \color{red}{-72x} +8 \\\Leftrightarrow & -189x \color{red}{+84} \color{blue}{-84} \color{blue}{+72x} & = & \color{red}{-72x} +8 \color{blue}{+72x} \color{blue}{-84} \\\Leftrightarrow & -189x+72x& = & 8-84 \\\Leftrightarrow & \color{red}{-117} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-117} & & \\\Leftrightarrow & x = \frac{76}{117} & & \\ & V = \left\{ \frac{76}{117} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 20x+\frac{10}{11}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+30} & = & \color{red}{231x} +55 \\\Leftrightarrow & 660x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & 660x-231x& = & 55-30 \\\Leftrightarrow & \color{red}{429} x& = & 25 \\\Leftrightarrow & x = \frac{25}{429} & & \\ & V = \left\{ \frac{25}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-50} & = & \color{red}{315x} +42 \\\Leftrightarrow & 140x \color{red}{-50} \color{blue}{+50} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+50} \\\Leftrightarrow & 140x-315x& = & 42+50 \\\Leftrightarrow & \color{red}{-175} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-175} & & \\\Leftrightarrow & x = \frac{-92}{175} & & \\ & V = \left\{ \frac{-92}{175} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 15x-\frac{15}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-135} & = & \color{red}{441x} +28 \\\Leftrightarrow & 945x \color{red}{-135} \color{blue}{+135} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+135} \\\Leftrightarrow & 945x-441x& = & 28+135 \\\Leftrightarrow & \color{red}{504} x& = & 163 \\\Leftrightarrow & x = \frac{163}{504} & & \\ & V = \left\{ \frac{163}{504} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{21}{10}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{+231} & = & \color{red}{-990x} +60 \\\Leftrightarrow & -3850x \color{red}{+231} \color{blue}{-231} \color{blue}{+990x} & = & \color{red}{-990x} +60 \color{blue}{+990x} \color{blue}{-231} \\\Leftrightarrow & -3850x+990x& = & 60-231 \\\Leftrightarrow & \color{red}{-2860} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{-2860} & & \\\Leftrightarrow & x = \frac{171}{2860} & & \\ & V = \left\{ \frac{171}{2860} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{8})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -35x+\frac{35}{8}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{385}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{72}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+385} & = & \color{red}{-792x} +72 \\\Leftrightarrow & -3080x \color{red}{+385} \color{blue}{-385} \color{blue}{+792x} & = & \color{red}{-792x} +72 \color{blue}{+792x} \color{blue}{-385} \\\Leftrightarrow & -3080x+792x& = & 72-385 \\\Leftrightarrow & \color{red}{-2288} x& = & -313 \\\Leftrightarrow & x = \frac{-313}{-2288} & & \\\Leftrightarrow & x = \frac{313}{2288} & & \\ & V = \left\{ \frac{313}{2288} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{6})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{35}{6}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-35} & = & \color{red}{-18x} +9 \\\Leftrightarrow & 168x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +9 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & 168x+18x& = & 9+35 \\\Leftrightarrow & \color{red}{186} x& = & 44 \\\Leftrightarrow & x = \frac{44}{186} & & \\\Leftrightarrow & x = \frac{22}{93} & & \\ & V = \left\{ \frac{22}{93} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+18} & = & \color{red}{75x} +25 \\\Leftrightarrow & 180x \color{red}{+18} \color{blue}{-18} \color{blue}{-75x} & = & \color{red}{75x} +25 \color{blue}{-75x} \color{blue}{-18} \\\Leftrightarrow & 180x-75x& = & 25-18 \\\Leftrightarrow & \color{red}{105} x& = & 7 \\\Leftrightarrow & x = \frac{7}{105} & & \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{10}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-360}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -360x \color{red}{+100} & = & \color{red}{810x} +27 \\\Leftrightarrow & -360x \color{red}{+100} \color{blue}{-100} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{-100} \\\Leftrightarrow & -360x-810x& = & 27-100 \\\Leftrightarrow & \color{red}{-1170} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-1170} & & \\\Leftrightarrow & x = \frac{73}{1170} & & \\ & V = \left\{ \frac{73}{1170} \right\} & \\\end{align}\)