Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{4})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -12x-\frac{9}{4}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x- \frac{99}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{-99} & = & \color{red}{220x} +32 \\\Leftrightarrow & -528x \color{red}{-99} \color{blue}{+99} \color{blue}{-220x} & = & \color{red}{220x} +32 \color{blue}{-220x} \color{blue}{+99} \\\Leftrightarrow & -528x-220x& = & 32+99 \\\Leftrightarrow & \color{red}{-748} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-748} & & \\\Leftrightarrow & x = \frac{-131}{748} & & \\ & V = \left\{ \frac{-131}{748} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{-90x} +36 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{+90x} & = & \color{red}{-90x} +36 \color{blue}{+90x} \color{blue}{+175} \\\Leftrightarrow & 420x+90x& = & 36+175 \\\Leftrightarrow & \color{red}{510} x& = & 211 \\\Leftrightarrow & x = \frac{211}{510} & & \\ & V = \left\{ \frac{211}{510} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-140} & = & \color{red}{105x} +18 \\\Leftrightarrow & -252x \color{red}{-140} \color{blue}{+140} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{+140} \\\Leftrightarrow & -252x-105x& = & 18+140 \\\Leftrightarrow & \color{red}{-357} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-357} & & \\\Leftrightarrow & x = \frac{-158}{357} & & \\ & V = \left\{ \frac{-158}{357} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{9})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+140} & = & \color{red}{189x} +18 \\\Leftrightarrow & 1260x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & 1260x-189x& = & 18-140 \\\Leftrightarrow & \color{red}{1071} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{1071} & & \\ & V = \left\{ \frac{-122}{1071} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{75x} +50 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-12} \\\Leftrightarrow & 120x-75x& = & 50-12 \\\Leftrightarrow & \color{red}{45} x& = & 38 \\\Leftrightarrow & x = \frac{38}{45} & & \\ & V = \left\{ \frac{38}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2112}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2112x \color{red}{+144} & = & \color{red}{-440x} +99 \\\Leftrightarrow & -2112x \color{red}{+144} \color{blue}{-144} \color{blue}{+440x} & = & \color{red}{-440x} +99 \color{blue}{+440x} \color{blue}{-144} \\\Leftrightarrow & -2112x+440x& = & 99-144 \\\Leftrightarrow & \color{red}{-1672} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-1672} & & \\\Leftrightarrow & x = \frac{45}{1672} & & \\ & V = \left\{ \frac{45}{1672} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{8}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{72}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-72} & = & \color{red}{315x} +40 \\\Leftrightarrow & -270x \color{red}{-72} \color{blue}{+72} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+72} \\\Leftrightarrow & -270x-315x& = & 40+72 \\\Leftrightarrow & \color{red}{-585} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-585} & & \\\Leftrightarrow & x = \frac{-112}{585} & & \\ & V = \left\{ \frac{-112}{585} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & -300x+70x& = & 35-48 \\\Leftrightarrow & \color{red}{-230} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-230} & & \\\Leftrightarrow & x = \frac{13}{230} & & \\ & V = \left\{ \frac{13}{230} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & 3x+\frac{7}{3} \\\Leftrightarrow & -8x-\frac{10}{3}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-10} & = & \color{red}{9x} +7 \\\Leftrightarrow & -24x \color{red}{-10} \color{blue}{+10} \color{blue}{-9x} & = & \color{red}{9x} +7 \color{blue}{-9x} \color{blue}{+10} \\\Leftrightarrow & -24x-9x& = & 7+10 \\\Leftrightarrow & \color{red}{-33} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-33} & & \\\Leftrightarrow & x = \frac{-17}{33} & & \\ & V = \left\{ \frac{-17}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{7})& = & -6x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{20}{7}& = & -6x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+60} & = & \color{red}{-126x} +28 \\\Leftrightarrow & 525x \color{red}{+60} \color{blue}{-60} \color{blue}{+126x} & = & \color{red}{-126x} +28 \color{blue}{+126x} \color{blue}{-60} \\\Leftrightarrow & 525x+126x& = & 28-60 \\\Leftrightarrow & \color{red}{651} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{651} & & \\ & V = \left\{ \frac{-32}{651} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-18} & = & \color{red}{35x} +6 \\\Leftrightarrow & -120x \color{red}{-18} \color{blue}{+18} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+18} \\\Leftrightarrow & -120x-35x& = & 6+18 \\\Leftrightarrow & \color{red}{-155} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-155} & & \\\Leftrightarrow & x = \frac{-24}{155} & & \\ & V = \left\{ \frac{-24}{155} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{-45} & = & \color{red}{-30x} +4 \\\Leftrightarrow & -72x \color{red}{-45} \color{blue}{+45} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{+45} \\\Leftrightarrow & -72x+30x& = & 4+45 \\\Leftrightarrow & \color{red}{-42} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-42} & & \\\Leftrightarrow & x = \frac{-7}{6} & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)