Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{2})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -25x-\frac{25}{2}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-50}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -50x \color{red}{-25} & = & \color{red}{-18x} +3 \\\Leftrightarrow & -50x \color{red}{-25} \color{blue}{+25} \color{blue}{+18x} & = & \color{red}{-18x} +3 \color{blue}{+18x} \color{blue}{+25} \\\Leftrightarrow & -50x+18x& = & 3+25 \\\Leftrightarrow & \color{red}{-32} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-32} & & \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{2})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{15}{2}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{80}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 80x \color{red}{-60} & = & \color{red}{24x} +7 \\\Leftrightarrow & 80x \color{red}{-60} \color{blue}{+60} \color{blue}{-24x} & = & \color{red}{24x} +7 \color{blue}{-24x} \color{blue}{+60} \\\Leftrightarrow & 80x-24x& = & 7+60 \\\Leftrightarrow & \color{red}{56} x& = & 67 \\\Leftrightarrow & x = \frac{67}{56} & & \\ & V = \left\{ \frac{67}{56} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 9x+\frac{9}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{+81} & = & \color{red}{441x} +56 \\\Leftrightarrow & 567x \color{red}{+81} \color{blue}{-81} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-81} \\\Leftrightarrow & 567x-441x& = & 56-81 \\\Leftrightarrow & \color{red}{126} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{126} & & \\ & V = \left\{ \frac{-25}{126} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -6x-\frac{8}{9}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{27}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-40} & = & \color{red}{315x} +27 \\\Leftrightarrow & -270x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +27 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -270x-315x& = & 27+40 \\\Leftrightarrow & \color{red}{-585} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-585} & & \\\Leftrightarrow & x = \frac{-67}{585} & & \\ & V = \left\{ \frac{-67}{585} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{8})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{25}{8}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-275} & = & \color{red}{264x} +80 \\\Leftrightarrow & 880x \color{red}{-275} \color{blue}{+275} \color{blue}{-264x} & = & \color{red}{264x} +80 \color{blue}{-264x} \color{blue}{+275} \\\Leftrightarrow & 880x-264x& = & 80+275 \\\Leftrightarrow & \color{red}{616} x& = & 355 \\\Leftrightarrow & x = \frac{355}{616} & & \\ & V = \left\{ \frac{355}{616} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & -3x+\frac{9}{5} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{-45x} +27 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{+45x} & = & \color{red}{-45x} +27 \color{blue}{+45x} \color{blue}{+40} \\\Leftrightarrow & -300x+45x& = & 27+40 \\\Leftrightarrow & \color{red}{-255} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-255} & & \\\Leftrightarrow & x = \frac{-67}{255} & & \\ & V = \left\{ \frac{-67}{255} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -21x+\frac{35}{9}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-756}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -756x \color{red}{+140} & = & \color{red}{288x} +27 \\\Leftrightarrow & -756x \color{red}{+140} \color{blue}{-140} \color{blue}{-288x} & = & \color{red}{288x} +27 \color{blue}{-288x} \color{blue}{-140} \\\Leftrightarrow & -756x-288x& = & 27-140 \\\Leftrightarrow & \color{red}{-1044} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-1044} & & \\\Leftrightarrow & x = \frac{113}{1044} & & \\ & V = \left\{ \frac{113}{1044} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+10} & = & \color{red}{-33x} +8 \\\Leftrightarrow & 220x \color{red}{+10} \color{blue}{-10} \color{blue}{+33x} & = & \color{red}{-33x} +8 \color{blue}{+33x} \color{blue}{-10} \\\Leftrightarrow & 220x+33x& = & 8-10 \\\Leftrightarrow & \color{red}{253} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{253} & & \\ & V = \left\{ \frac{-2}{253} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-147x} +35 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+147x} & = & \color{red}{-147x} +35 \color{blue}{+147x} \color{blue}{+30} \\\Leftrightarrow & -210x+147x& = & 35+30 \\\Leftrightarrow & \color{red}{-63} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-63} & & \\\Leftrightarrow & x = \frac{-65}{63} & & \\ & V = \left\{ \frac{-65}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 120x+25x& = & 4-24 \\\Leftrightarrow & \color{red}{145} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{145} & & \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{11})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{16}{11}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+48} & = & \color{red}{-99x} +77 \\\Leftrightarrow & 660x \color{red}{+48} \color{blue}{-48} \color{blue}{+99x} & = & \color{red}{-99x} +77 \color{blue}{+99x} \color{blue}{-48} \\\Leftrightarrow & 660x+99x& = & 77-48 \\\Leftrightarrow & \color{red}{759} x& = & 29 \\\Leftrightarrow & x = \frac{29}{759} & & \\ & V = \left\{ \frac{29}{759} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{9})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{20}{9}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+140} & = & \color{red}{-315x} +90 \\\Leftrightarrow & -756x \color{red}{+140} \color{blue}{-140} \color{blue}{+315x} & = & \color{red}{-315x} +90 \color{blue}{+315x} \color{blue}{-140} \\\Leftrightarrow & -756x+315x& = & 90-140 \\\Leftrightarrow & \color{red}{-441} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-441} & & \\\Leftrightarrow & x = \frac{50}{441} & & \\ & V = \left\{ \frac{50}{441} \right\} & \\\end{align}\)