Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{441x} +28 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & -630x-441x& = & 28-90 \\\Leftrightarrow & \color{red}{-1071} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-1071} & & \\\Leftrightarrow & x = \frac{62}{1071} & & \\ & V = \left\{ \frac{62}{1071} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{9})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -21x+\frac{14}{9}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+14} & = & \color{red}{-72x} +4 \\\Leftrightarrow & -189x \color{red}{+14} \color{blue}{-14} \color{blue}{+72x} & = & \color{red}{-72x} +4 \color{blue}{+72x} \color{blue}{-14} \\\Leftrightarrow & -189x+72x& = & 4-14 \\\Leftrightarrow & \color{red}{-117} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-117} & & \\\Leftrightarrow & x = \frac{10}{117} & & \\ & V = \left\{ \frac{10}{117} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{3})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -6x-\frac{4}{3}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{12}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-12} & = & \color{red}{63x} +7 \\\Leftrightarrow & -54x \color{red}{-12} \color{blue}{+12} \color{blue}{-63x} & = & \color{red}{63x} +7 \color{blue}{-63x} \color{blue}{+12} \\\Leftrightarrow & -54x-63x& = & 7+12 \\\Leftrightarrow & \color{red}{-117} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-117} & & \\\Leftrightarrow & x = \frac{-19}{117} & & \\ & V = \left\{ \frac{-19}{117} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-40} & = & \color{red}{54x} +5 \\\Leftrightarrow & -48x \color{red}{-40} \color{blue}{+40} \color{blue}{-54x} & = & \color{red}{54x} +5 \color{blue}{-54x} \color{blue}{+40} \\\Leftrightarrow & -48x-54x& = & 5+40 \\\Leftrightarrow & \color{red}{-102} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-102} & & \\\Leftrightarrow & x = \frac{-15}{34} & & \\ & V = \left\{ \frac{-15}{34} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -16x+\frac{8}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+40} & = & \color{red}{385x} +88 \\\Leftrightarrow & -880x \color{red}{+40} \color{blue}{-40} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{-40} \\\Leftrightarrow & -880x-385x& = & 88-40 \\\Leftrightarrow & \color{red}{-1265} x& = & 48 \\\Leftrightarrow & x = \frac{48}{-1265} & & \\\Leftrightarrow & x = \frac{-48}{1265} & & \\ & V = \left\{ \frac{-48}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{4})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+105} & = & \color{red}{196x} +12 \\\Leftrightarrow & 700x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +12 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & 700x-196x& = & 12-105 \\\Leftrightarrow & \color{red}{504} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{504} & & \\\Leftrightarrow & x = \frac{-31}{168} & & \\ & V = \left\{ \frac{-31}{168} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{2})& = & -2x+\frac{8}{9} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{450}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{-36}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 450x \color{red}{+225} & = & \color{red}{-36x} +16 \\\Leftrightarrow & 450x \color{red}{+225} \color{blue}{-225} \color{blue}{+36x} & = & \color{red}{-36x} +16 \color{blue}{+36x} \color{blue}{-225} \\\Leftrightarrow & 450x+36x& = & 16-225 \\\Leftrightarrow & \color{red}{486} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{486} & & \\ & V = \left\{ \frac{-209}{486} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-9} & = & \color{red}{10x} +4 \\\Leftrightarrow & 45x \color{red}{-9} \color{blue}{+9} \color{blue}{-10x} & = & \color{red}{10x} +4 \color{blue}{-10x} \color{blue}{+9} \\\Leftrightarrow & 45x-10x& = & 4+9 \\\Leftrightarrow & \color{red}{35} x& = & 13 \\\Leftrightarrow & x = \frac{13}{35} & & \\ & V = \left\{ \frac{13}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{-231x} +56 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +56 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & 770x+231x& = & 56+110 \\\Leftrightarrow & \color{red}{1001} x& = & 166 \\\Leftrightarrow & x = \frac{166}{1001} & & \\ & V = \left\{ \frac{166}{1001} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+16} & = & \color{red}{-21x} +2 \\\Leftrightarrow & 140x \color{red}{+16} \color{blue}{-16} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{-16} \\\Leftrightarrow & 140x+21x& = & 2-16 \\\Leftrightarrow & \color{red}{161} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{161} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 126x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 126x-105x& = & 56-18 \\\Leftrightarrow & \color{red}{21} x& = & 38 \\\Leftrightarrow & x = \frac{38}{21} & & \\ & V = \left\{ \frac{38}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+210} & = & \color{red}{385x} +66 \\\Leftrightarrow & 1386x \color{red}{+210} \color{blue}{-210} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-210} \\\Leftrightarrow & 1386x-385x& = & 66-210 \\\Leftrightarrow & \color{red}{1001} x& = & -144 \\\Leftrightarrow & x = \frac{-144}{1001} & & \\ & V = \left\{ \frac{-144}{1001} \right\} & \\\end{align}\)