Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & -12x+\frac{15}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+135} & = & \color{red}{315x} +35 \\\Leftrightarrow & -756x \color{red}{+135} \color{blue}{-135} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-135} \\\Leftrightarrow & -756x-315x& = & 35-135 \\\Leftrightarrow & \color{red}{-1071} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-1071} & & \\\Leftrightarrow & x = \frac{100}{1071} & & \\ & V = \left\{ \frac{100}{1071} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{-14} & = & \color{red}{15x} +10 \\\Leftrightarrow & 42x \color{red}{-14} \color{blue}{+14} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{+14} \\\Leftrightarrow & 42x-15x& = & 10+14 \\\Leftrightarrow & \color{red}{27} x& = & 24 \\\Leftrightarrow & x = \frac{24}{27} & & \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{2})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -20x+\frac{25}{2}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+175} & = & \color{red}{-98x} +16 \\\Leftrightarrow & -280x \color{red}{+175} \color{blue}{-175} \color{blue}{+98x} & = & \color{red}{-98x} +16 \color{blue}{+98x} \color{blue}{-175} \\\Leftrightarrow & -280x+98x& = & 16-175 \\\Leftrightarrow & \color{red}{-182} x& = & -159 \\\Leftrightarrow & x = \frac{-159}{-182} & & \\\Leftrightarrow & x = \frac{159}{182} & & \\ & V = \left\{ \frac{159}{182} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -300x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{-195} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-195} & & \\\Leftrightarrow & x = \frac{-56}{195} & & \\ & V = \left\{ \frac{-56}{195} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -35x+\frac{35}{3}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{108x} +27 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{-108x} & = & \color{red}{108x} +27 \color{blue}{-108x} \color{blue}{-140} \\\Leftrightarrow & -420x-108x& = & 27-140 \\\Leftrightarrow & \color{red}{-528} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-528} & & \\\Leftrightarrow & x = \frac{113}{528} & & \\ & V = \left\{ \frac{113}{528} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-42} & = & \color{red}{81x} +8 \\\Leftrightarrow & 252x \color{red}{-42} \color{blue}{+42} \color{blue}{-81x} & = & \color{red}{81x} +8 \color{blue}{-81x} \color{blue}{+42} \\\Leftrightarrow & 252x-81x& = & 8+42 \\\Leftrightarrow & \color{red}{171} x& = & 50 \\\Leftrightarrow & x = \frac{50}{171} & & \\ & V = \left\{ \frac{50}{171} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{231x} +22 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & -330x-231x& = & 22+30 \\\Leftrightarrow & \color{red}{-561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-561} & & \\\Leftrightarrow & x = \frac{-52}{561} & & \\ & V = \left\{ \frac{-52}{561} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{9})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+80} & = & \color{red}{252x} +81 \\\Leftrightarrow & 540x \color{red}{+80} \color{blue}{-80} \color{blue}{-252x} & = & \color{red}{252x} +81 \color{blue}{-252x} \color{blue}{-80} \\\Leftrightarrow & 540x-252x& = & 81-80 \\\Leftrightarrow & \color{red}{288} x& = & 1 \\\Leftrightarrow & x = \frac{1}{288} & & \\ & V = \left\{ \frac{1}{288} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{16}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-48} \\\Leftrightarrow & 396x+165x& = & 22-48 \\\Leftrightarrow & \color{red}{561} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{561} & & \\ & V = \left\{ \frac{-26}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{9})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{25}{9}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{175}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-175} & = & \color{red}{-504x} +81 \\\Leftrightarrow & -945x \color{red}{-175} \color{blue}{+175} \color{blue}{+504x} & = & \color{red}{-504x} +81 \color{blue}{+504x} \color{blue}{+175} \\\Leftrightarrow & -945x+504x& = & 81+175 \\\Leftrightarrow & \color{red}{-441} x& = & 256 \\\Leftrightarrow & x = \frac{256}{-441} & & \\\Leftrightarrow & x = \frac{-256}{441} & & \\ & V = \left\{ \frac{-256}{441} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+42} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -525x \color{red}{+42} \color{blue}{-42} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{-42} \\\Leftrightarrow & -525x+135x& = & 10-42 \\\Leftrightarrow & \color{red}{-390} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-390} & & \\\Leftrightarrow & x = \frac{16}{195} & & \\ & V = \left\{ \frac{16}{195} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{15}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-198}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -198x \color{red}{-30} & = & \color{red}{110x} +33 \\\Leftrightarrow & -198x \color{red}{-30} \color{blue}{+30} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{+30} \\\Leftrightarrow & -198x-110x& = & 33+30 \\\Leftrightarrow & \color{red}{-308} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-308} & & \\\Leftrightarrow & x = \frac{-9}{44} & & \\ & V = \left\{ \frac{-9}{44} \right\} & \\\end{align}\)