Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{2})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{9}{2}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-48}{ \color{blue}{4} }x- \frac{18}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -48x \color{red}{-18} & = & \color{red}{20x} +3 \\\Leftrightarrow & -48x \color{red}{-18} \color{blue}{+18} \color{blue}{-20x} & = & \color{red}{20x} +3 \color{blue}{-20x} \color{blue}{+18} \\\Leftrightarrow & -48x-20x& = & 3+18 \\\Leftrightarrow & \color{red}{-68} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-68} & & \\\Leftrightarrow & x = \frac{-21}{68} & & \\ & V = \left\{ \frac{-21}{68} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{9}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +9 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +9 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 9-12 \\\Leftrightarrow & \color{red}{-85} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-85} & & \\\Leftrightarrow & x = \frac{3}{85} & & \\ & V = \left\{ \frac{3}{85} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & -4x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{15}{8}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{-32x} +12 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{+32x} & = & \color{red}{-32x} +12 \color{blue}{+32x} \color{blue}{+15} \\\Leftrightarrow & 120x+32x& = & 12+15 \\\Leftrightarrow & \color{red}{152} x& = & 27 \\\Leftrightarrow & x = \frac{27}{152} & & \\ & V = \left\{ \frac{27}{152} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-192}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -192x \color{red}{+80} & = & \color{red}{84x} +27 \\\Leftrightarrow & -192x \color{red}{+80} \color{blue}{-80} \color{blue}{-84x} & = & \color{red}{84x} +27 \color{blue}{-84x} \color{blue}{-80} \\\Leftrightarrow & -192x-84x& = & 27-80 \\\Leftrightarrow & \color{red}{-276} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-276} & & \\\Leftrightarrow & x = \frac{53}{276} & & \\ & V = \left\{ \frac{53}{276} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+150} & = & \color{red}{275x} +22 \\\Leftrightarrow & 990x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & 990x-275x& = & 22-150 \\\Leftrightarrow & \color{red}{715} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{715} & & \\ & V = \left\{ \frac{-128}{715} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{20}{3}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+100} & = & \color{red}{-105x} +24 \\\Leftrightarrow & -150x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -150x+105x& = & 24-100 \\\Leftrightarrow & \color{red}{-45} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-45} & & \\\Leftrightarrow & x = \frac{76}{45} & & \\ & V = \left\{ \frac{76}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{-693x} +42 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -308x+693x& = & 42+110 \\\Leftrightarrow & \color{red}{385} x& = & 152 \\\Leftrightarrow & x = \frac{152}{385} & & \\ & V = \left\{ \frac{152}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{1}{2})& = & 3x+\frac{5}{8} \\\Leftrightarrow & 14x-\frac{7}{2}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{28}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-28} & = & \color{red}{24x} +5 \\\Leftrightarrow & 112x \color{red}{-28} \color{blue}{+28} \color{blue}{-24x} & = & \color{red}{24x} +5 \color{blue}{-24x} \color{blue}{+28} \\\Leftrightarrow & 112x-24x& = & 5+28 \\\Leftrightarrow & \color{red}{88} x& = & 33 \\\Leftrightarrow & x = \frac{33}{88} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{4})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -12x+\frac{9}{4}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+18} & = & \color{red}{-40x} +9 \\\Leftrightarrow & -96x \color{red}{+18} \color{blue}{-18} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{-18} \\\Leftrightarrow & -96x+40x& = & 9-18 \\\Leftrightarrow & \color{red}{-56} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-56} & & \\\Leftrightarrow & x = \frac{9}{56} & & \\ & V = \left\{ \frac{9}{56} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1680}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1680x \color{red}{+300} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -1680x \color{red}{+300} \color{blue}{-300} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-300} \\\Leftrightarrow & -1680x+350x& = & 63-300 \\\Leftrightarrow & \color{red}{-1330} x& = & -237 \\\Leftrightarrow & x = \frac{-237}{-1330} & & \\\Leftrightarrow & x = \frac{237}{1330} & & \\ & V = \left\{ \frac{237}{1330} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{9})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{35}{9}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+35} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 126x \color{red}{+35} \color{blue}{-35} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{-35} \\\Leftrightarrow & 126x+81x& = & 10-35 \\\Leftrightarrow & \color{red}{207} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{207} & & \\ & V = \left\{ \frac{-25}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 21x-\frac{28}{5}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-84} & = & \color{red}{30x} +40 \\\Leftrightarrow & 315x \color{red}{-84} \color{blue}{+84} \color{blue}{-30x} & = & \color{red}{30x} +40 \color{blue}{-30x} \color{blue}{+84} \\\Leftrightarrow & 315x-30x& = & 40+84 \\\Leftrightarrow & \color{red}{285} x& = & 124 \\\Leftrightarrow & x = \frac{124}{285} & & \\ & V = \left\{ \frac{124}{285} \right\} & \\\end{align}\)