Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{10}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+110} & = & \color{red}{-99x} +18 \\\Leftrightarrow & -660x \color{red}{+110} \color{blue}{-110} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{-110} \\\Leftrightarrow & -660x+99x& = & 18-110 \\\Leftrightarrow & \color{red}{-561} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-561} & & \\\Leftrightarrow & x = \frac{92}{561} & & \\ & V = \left\{ \frac{92}{561} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{4})& = & -9x+\frac{9}{5} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{-180x} +36 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{+180x} & = & \color{red}{-180x} +36 \color{blue}{+180x} \color{blue}{-75} \\\Leftrightarrow & 400x+180x& = & 36-75 \\\Leftrightarrow & \color{red}{580} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{580} & & \\ & V = \left\{ \frac{-39}{580} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{9})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+40} & = & \color{red}{126x} +15 \\\Leftrightarrow & 270x \color{red}{+40} \color{blue}{-40} \color{blue}{-126x} & = & \color{red}{126x} +15 \color{blue}{-126x} \color{blue}{-40} \\\Leftrightarrow & 270x-126x& = & 15-40 \\\Leftrightarrow & \color{red}{144} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{144} & & \\ & V = \left\{ \frac{-25}{144} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{7})& = & -8x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{15}{7}& = & -8x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-112x} +49 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+112x} & = & \color{red}{-112x} +49 \color{blue}{+112x} \color{blue}{-30} \\\Leftrightarrow & -210x+112x& = & 49-30 \\\Leftrightarrow & \color{red}{-98} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-98} & & \\\Leftrightarrow & x = \frac{-19}{98} & & \\ & V = \left\{ \frac{-19}{98} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{25}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{275}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-275} & = & \color{red}{-231x} +18 \\\Leftrightarrow & 495x \color{red}{-275} \color{blue}{+275} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{+275} \\\Leftrightarrow & 495x+231x& = & 18+275 \\\Leftrightarrow & \color{red}{726} x& = & 293 \\\Leftrightarrow & x = \frac{293}{726} & & \\ & V = \left\{ \frac{293}{726} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{5})& = & -5x+\frac{3}{11} \\\Leftrightarrow & -24x+\frac{18}{5}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+198} & = & \color{red}{-275x} +15 \\\Leftrightarrow & -1320x \color{red}{+198} \color{blue}{-198} \color{blue}{+275x} & = & \color{red}{-275x} +15 \color{blue}{+275x} \color{blue}{-198} \\\Leftrightarrow & -1320x+275x& = & 15-198 \\\Leftrightarrow & \color{red}{-1045} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{-1045} & & \\\Leftrightarrow & x = \frac{183}{1045} & & \\ & V = \left\{ \frac{183}{1045} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{9})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 16x+\frac{8}{9}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1152}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1152x \color{red}{+64} & = & \color{red}{-648x} +63 \\\Leftrightarrow & 1152x \color{red}{+64} \color{blue}{-64} \color{blue}{+648x} & = & \color{red}{-648x} +63 \color{blue}{+648x} \color{blue}{-64} \\\Leftrightarrow & 1152x+648x& = & 63-64 \\\Leftrightarrow & \color{red}{1800} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1800} & & \\ & V = \left\{ \frac{-1}{1800} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{3})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{8}{3}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & -90x+105x& = & 6-40 \\\Leftrightarrow & \color{red}{15} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{15} & & \\ & V = \left\{ \frac{-34}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 30x+\frac{12}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+60} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 1650x \color{red}{+60} \color{blue}{-60} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-60} \\\Leftrightarrow & 1650x+385x& = & 88-60 \\\Leftrightarrow & \color{red}{2035} x& = & 28 \\\Leftrightarrow & x = \frac{28}{2035} & & \\ & V = \left\{ \frac{28}{2035} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +10 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 10+132 \\\Leftrightarrow & \color{red}{-935} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-935} & & \\\Leftrightarrow & x = \frac{-142}{935} & & \\ & V = \left\{ \frac{-142}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{-64} & = & \color{red}{168x} +15 \\\Leftrightarrow & -240x \color{red}{-64} \color{blue}{+64} \color{blue}{-168x} & = & \color{red}{168x} +15 \color{blue}{-168x} \color{blue}{+64} \\\Leftrightarrow & -240x-168x& = & 15+64 \\\Leftrightarrow & \color{red}{-408} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-408} & & \\\Leftrightarrow & x = \frac{-79}{408} & & \\ & V = \left\{ \frac{-79}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -9x+\frac{15}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+105} & = & \color{red}{385x} +99 \\\Leftrightarrow & -693x \color{red}{+105} \color{blue}{-105} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{-105} \\\Leftrightarrow & -693x-385x& = & 99-105 \\\Leftrightarrow & \color{red}{-1078} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-1078} & & \\\Leftrightarrow & x = \frac{3}{539} & & \\ & V = \left\{ \frac{3}{539} \right\} & \\\end{align}\)