Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{9})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{35}{9}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{-225x} +72 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{+225x} & = & \color{red}{-225x} +72 \color{blue}{+225x} \color{blue}{+175} \\\Leftrightarrow & 630x+225x& = & 72+175 \\\Leftrightarrow & \color{red}{855} x& = & 247 \\\Leftrightarrow & x = \frac{247}{855} & & \\\Leftrightarrow & x = \frac{13}{45} & & \\ & V = \left\{ \frac{13}{45} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -14x-\frac{14}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{18x} +9 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+28} \\\Leftrightarrow & -84x-18x& = & 9+28 \\\Leftrightarrow & \color{red}{-102} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-102} & & \\\Leftrightarrow & x = \frac{-37}{102} & & \\ & V = \left\{ \frac{-37}{102} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 675x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & 675x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{990} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{990} & & \\\Leftrightarrow & x = \frac{-29}{495} & & \\ & V = \left\{ \frac{-29}{495} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -3x+\frac{9}{11} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+110} & = & \color{red}{-231x} +63 \\\Leftrightarrow & 308x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +63 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & 308x+231x& = & 63-110 \\\Leftrightarrow & \color{red}{539} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{539} & & \\ & V = \left\{ \frac{-47}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{35}{9}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x+ \frac{175}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{+175} & = & \color{red}{360x} +54 \\\Leftrightarrow & -945x \color{red}{+175} \color{blue}{-175} \color{blue}{-360x} & = & \color{red}{360x} +54 \color{blue}{-360x} \color{blue}{-175} \\\Leftrightarrow & -945x-360x& = & 54-175 \\\Leftrightarrow & \color{red}{-1305} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{-1305} & & \\\Leftrightarrow & x = \frac{121}{1305} & & \\ & V = \left\{ \frac{121}{1305} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{9})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{4}{9}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+16} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -216x \color{red}{+16} \color{blue}{-16} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-16} \\\Leftrightarrow & -216x+252x& = & 21-16 \\\Leftrightarrow & \color{red}{36} x& = & 5 \\\Leftrightarrow & x = \frac{5}{36} & & \\ & V = \left\{ \frac{5}{36} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-630}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -630x \color{red}{+120} & = & \color{red}{168x} +35 \\\Leftrightarrow & -630x \color{red}{+120} \color{blue}{-120} \color{blue}{-168x} & = & \color{red}{168x} +35 \color{blue}{-168x} \color{blue}{-120} \\\Leftrightarrow & -630x-168x& = & 35-120 \\\Leftrightarrow & \color{red}{-798} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-798} & & \\\Leftrightarrow & x = \frac{85}{798} & & \\ & V = \left\{ \frac{85}{798} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & 9x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 9x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-32} & = & \color{red}{108x} +21 \\\Leftrightarrow & 120x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +21 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & 120x-108x& = & 21+32 \\\Leftrightarrow & \color{red}{12} x& = & 53 \\\Leftrightarrow & x = \frac{53}{12} & & \\ & V = \left\{ \frac{53}{12} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -150x+35x& = & 6-12 \\\Leftrightarrow & \color{red}{-115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-115} & & \\\Leftrightarrow & x = \frac{6}{115} & & \\ & V = \left\{ \frac{6}{115} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+6} & = & \color{red}{77x} +10 \\\Leftrightarrow & 66x \color{red}{+6} \color{blue}{-6} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{-6} \\\Leftrightarrow & 66x-77x& = & 10-6 \\\Leftrightarrow & \color{red}{-11} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-11} & & \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{12}{11}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+24} & = & \color{red}{198x} +55 \\\Leftrightarrow & 440x \color{red}{+24} \color{blue}{-24} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{-24} \\\Leftrightarrow & 440x-198x& = & 55-24 \\\Leftrightarrow & \color{red}{242} x& = & 31 \\\Leftrightarrow & x = \frac{31}{242} & & \\ & V = \left\{ \frac{31}{242} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{7})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 18x-\frac{24}{7}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1512}{ \color{blue}{84} }x- \frac{288}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1512x \color{red}{-288} & = & \color{red}{-420x} +49 \\\Leftrightarrow & 1512x \color{red}{-288} \color{blue}{+288} \color{blue}{+420x} & = & \color{red}{-420x} +49 \color{blue}{+420x} \color{blue}{+288} \\\Leftrightarrow & 1512x+420x& = & 49+288 \\\Leftrightarrow & \color{red}{1932} x& = & 337 \\\Leftrightarrow & x = \frac{337}{1932} & & \\ & V = \left\{ \frac{337}{1932} \right\} & \\\end{align}\)