Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & -660x-275x& = & 22+90 \\\Leftrightarrow & \color{red}{-935} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-935} & & \\\Leftrightarrow & x = \frac{-112}{935} & & \\ & V = \left\{ \frac{-112}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{9})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -8x-\frac{20}{9}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-140} & = & \color{red}{-567x} +54 \\\Leftrightarrow & -504x \color{red}{-140} \color{blue}{+140} \color{blue}{+567x} & = & \color{red}{-567x} +54 \color{blue}{+567x} \color{blue}{+140} \\\Leftrightarrow & -504x+567x& = & 54+140 \\\Leftrightarrow & \color{red}{63} x& = & 194 \\\Leftrightarrow & x = \frac{194}{63} & & \\ & V = \left\{ \frac{194}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{-441x} +28 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & 504x+441x& = & 28-54 \\\Leftrightarrow & \color{red}{945} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{945} & & \\ & V = \left\{ \frac{-26}{945} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -84x+35x& = & 8+30 \\\Leftrightarrow & \color{red}{-49} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-49} & & \\\Leftrightarrow & x = \frac{-38}{49} & & \\ & V = \left\{ \frac{-38}{49} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 4x-\frac{8}{9}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{-8} & = & \color{red}{-45x} +5 \\\Leftrightarrow & 36x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +5 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & 36x+45x& = & 5+8 \\\Leftrightarrow & \color{red}{81} x& = & 13 \\\Leftrightarrow & x = \frac{13}{81} & & \\ & V = \left\{ \frac{13}{81} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{9})& = & 9x+\frac{7}{4} \\\Leftrightarrow & 28x+\frac{35}{9}& = & 9x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x+ \frac{140}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{+140} & = & \color{red}{324x} +63 \\\Leftrightarrow & 1008x \color{red}{+140} \color{blue}{-140} \color{blue}{-324x} & = & \color{red}{324x} +63 \color{blue}{-324x} \color{blue}{-140} \\\Leftrightarrow & 1008x-324x& = & 63-140 \\\Leftrightarrow & \color{red}{684} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{684} & & \\ & V = \left\{ \frac{-77}{684} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{10}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{+40} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 72x \color{red}{+40} \color{blue}{-40} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{-40} \\\Leftrightarrow & 72x+60x& = & 27-40 \\\Leftrightarrow & \color{red}{132} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{132} & & \\ & V = \left\{ \frac{-13}{132} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{6}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{105x} +40 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 150x-105x& = & 40+18 \\\Leftrightarrow & \color{red}{45} x& = & 58 \\\Leftrightarrow & x = \frac{58}{45} & & \\ & V = \left\{ \frac{58}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-120} & = & \color{red}{275x} +88 \\\Leftrightarrow & -660x \color{red}{-120} \color{blue}{+120} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{+120} \\\Leftrightarrow & -660x-275x& = & 88+120 \\\Leftrightarrow & \color{red}{-935} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-935} & & \\\Leftrightarrow & x = \frac{-208}{935} & & \\ & V = \left\{ \frac{-208}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -30x-\frac{18}{7}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x- \frac{108}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{-108} & = & \color{red}{-294x} +49 \\\Leftrightarrow & -1260x \color{red}{-108} \color{blue}{+108} \color{blue}{+294x} & = & \color{red}{-294x} +49 \color{blue}{+294x} \color{blue}{+108} \\\Leftrightarrow & -1260x+294x& = & 49+108 \\\Leftrightarrow & \color{red}{-966} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-966} & & \\\Leftrightarrow & x = \frac{-157}{966} & & \\ & V = \left\{ \frac{-157}{966} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{18}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{90}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+90} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{+90} \color{blue}{-90} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-90} \\\Leftrightarrow & -420x-175x& = & 42-90 \\\Leftrightarrow & \color{red}{-595} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-595} & & \\\Leftrightarrow & x = \frac{48}{595} & & \\ & V = \left\{ \frac{48}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{3})& = & -9x+\frac{3}{4} \\\Leftrightarrow & 28x+\frac{7}{3}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{+28} & = & \color{red}{-108x} +9 \\\Leftrightarrow & 336x \color{red}{+28} \color{blue}{-28} \color{blue}{+108x} & = & \color{red}{-108x} +9 \color{blue}{+108x} \color{blue}{-28} \\\Leftrightarrow & 336x+108x& = & 9-28 \\\Leftrightarrow & \color{red}{444} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{444} & & \\ & V = \left\{ \frac{-19}{444} \right\} & \\\end{align}\)