Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 28x+\frac{35}{4}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x+ \frac{315}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{+315} & = & \color{red}{-324x} +8 \\\Leftrightarrow & 1008x \color{red}{+315} \color{blue}{-315} \color{blue}{+324x} & = & \color{red}{-324x} +8 \color{blue}{+324x} \color{blue}{-315} \\\Leftrightarrow & 1008x+324x& = & 8-315 \\\Leftrightarrow & \color{red}{1332} x& = & -307 \\\Leftrightarrow & x = \frac{-307}{1332} & & \\ & V = \left\{ \frac{-307}{1332} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+8} & = & \color{red}{-9x} +10 \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{-8} \\\Leftrightarrow & -24x+9x& = & 10-8 \\\Leftrightarrow & \color{red}{-15} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-15} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{9}{2}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{27}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-27} & = & \color{red}{48x} +8 \\\Leftrightarrow & 90x \color{red}{-27} \color{blue}{+27} \color{blue}{-48x} & = & \color{red}{48x} +8 \color{blue}{-48x} \color{blue}{+27} \\\Leftrightarrow & 90x-48x& = & 8+27 \\\Leftrightarrow & \color{red}{42} x& = & 35 \\\Leftrightarrow & x = \frac{35}{42} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{9})& = & 3x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{4}{9}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-28} & = & \color{red}{189x} +18 \\\Leftrightarrow & -504x \color{red}{-28} \color{blue}{+28} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{+28} \\\Leftrightarrow & -504x-189x& = & 18+28 \\\Leftrightarrow & \color{red}{-693} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-693} & & \\\Leftrightarrow & x = \frac{-46}{693} & & \\ & V = \left\{ \frac{-46}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1680}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1680x \color{red}{+240} & = & \color{red}{392x} +63 \\\Leftrightarrow & 1680x \color{red}{+240} \color{blue}{-240} \color{blue}{-392x} & = & \color{red}{392x} +63 \color{blue}{-392x} \color{blue}{-240} \\\Leftrightarrow & 1680x-392x& = & 63-240 \\\Leftrightarrow & \color{red}{1288} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{1288} & & \\ & V = \left\{ \frac{-177}{1288} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{25x} +2 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{-6} \\\Leftrightarrow & 30x-25x& = & 2-6 \\\Leftrightarrow & \color{red}{5} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-1)& = & 4x+\frac{9}{11} \\\Leftrightarrow & 35x+7& = & 4x+\frac{9}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{77}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+77} & = & \color{red}{44x} +9 \\\Leftrightarrow & 385x \color{red}{+77} \color{blue}{-77} \color{blue}{-44x} & = & \color{red}{44x} +9 \color{blue}{-44x} \color{blue}{-77} \\\Leftrightarrow & 385x-44x& = & 9-77 \\\Leftrightarrow & \color{red}{341} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{341} & & \\ & V = \left\{ \frac{-68}{341} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{7})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+16} & = & \color{red}{-126x} +35 \\\Leftrightarrow & 112x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & 112x+126x& = & 35-16 \\\Leftrightarrow & \color{red}{238} x& = & 19 \\\Leftrightarrow & x = \frac{19}{238} & & \\ & V = \left\{ \frac{19}{238} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{-935} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-935} & & \\\Leftrightarrow & x = \frac{107}{935} & & \\ & V = \left\{ \frac{107}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{11})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -35x-\frac{28}{11}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-2310}{ \color{blue}{66} }x- \frac{168}{ \color{blue}{66} })& = & (\frac{198}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -2310x \color{red}{-168} & = & \color{red}{198x} +55 \\\Leftrightarrow & -2310x \color{red}{-168} \color{blue}{+168} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{+168} \\\Leftrightarrow & -2310x-198x& = & 55+168 \\\Leftrightarrow & \color{red}{-2508} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-2508} & & \\\Leftrightarrow & x = \frac{-223}{2508} & & \\ & V = \left\{ \frac{-223}{2508} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{98x} +49 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+12} \\\Leftrightarrow & 84x-98x& = & 49+12 \\\Leftrightarrow & \color{red}{-14} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-14} & & \\\Leftrightarrow & x = \frac{-61}{14} & & \\ & V = \left\{ \frac{-61}{14} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -14x-\frac{14}{3}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-98} & = & \color{red}{105x} +27 \\\Leftrightarrow & -294x \color{red}{-98} \color{blue}{+98} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{+98} \\\Leftrightarrow & -294x-105x& = & 27+98 \\\Leftrightarrow & \color{red}{-399} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-399} & & \\\Leftrightarrow & x = \frac{-125}{399} & & \\ & V = \left\{ \frac{-125}{399} \right\} & \\\end{align}\)