Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & 3x+\frac{7}{5} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 3x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{45x} +21 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-45x} & = & \color{red}{45x} +21 \color{blue}{-45x} \color{blue}{-40} \\\Leftrightarrow & 120x-45x& = & 21-40 \\\Leftrightarrow & \color{red}{75} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{75} & & \\ & V = \left\{ \frac{-19}{75} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{-595} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-595} & & \\\Leftrightarrow & x = \frac{-134}{595} & & \\ & V = \left\{ \frac{-134}{595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{6})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 28x+\frac{35}{6}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+105} & = & \color{red}{-162x} +16 \\\Leftrightarrow & 504x \color{red}{+105} \color{blue}{-105} \color{blue}{+162x} & = & \color{red}{-162x} +16 \color{blue}{+162x} \color{blue}{-105} \\\Leftrightarrow & 504x+162x& = & 16-105 \\\Leftrightarrow & \color{red}{666} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{666} & & \\ & V = \left\{ \frac{-89}{666} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{11})& = & 8x+\frac{9}{7} \\\Leftrightarrow & -21x+\frac{35}{11}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{+245} & = & \color{red}{616x} +99 \\\Leftrightarrow & -1617x \color{red}{+245} \color{blue}{-245} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{-245} \\\Leftrightarrow & -1617x-616x& = & 99-245 \\\Leftrightarrow & \color{red}{-2233} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{-2233} & & \\\Leftrightarrow & x = \frac{146}{2233} & & \\ & V = \left\{ \frac{146}{2233} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{11})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -35x+\frac{14}{11}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x+ \frac{98}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{+98} & = & \color{red}{-693x} +99 \\\Leftrightarrow & -2695x \color{red}{+98} \color{blue}{-98} \color{blue}{+693x} & = & \color{red}{-693x} +99 \color{blue}{+693x} \color{blue}{-98} \\\Leftrightarrow & -2695x+693x& = & 99-98 \\\Leftrightarrow & \color{red}{-2002} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-2002} & & \\\Leftrightarrow & x = \frac{-1}{2002} & & \\ & V = \left\{ \frac{-1}{2002} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{7})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 12x-\frac{8}{7}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-40} & = & \color{red}{175x} +63 \\\Leftrightarrow & 420x \color{red}{-40} \color{blue}{+40} \color{blue}{-175x} & = & \color{red}{175x} +63 \color{blue}{-175x} \color{blue}{+40} \\\Leftrightarrow & 420x-175x& = & 63+40 \\\Leftrightarrow & \color{red}{245} x& = & 103 \\\Leftrightarrow & x = \frac{103}{245} & & \\ & V = \left\{ \frac{103}{245} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{16}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x- \frac{128}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{-128} & = & \color{red}{-440x} +77 \\\Leftrightarrow & 1056x \color{red}{-128} \color{blue}{+128} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{+128} \\\Leftrightarrow & 1056x+440x& = & 77+128 \\\Leftrightarrow & \color{red}{1496} x& = & 205 \\\Leftrightarrow & x = \frac{205}{1496} & & \\ & V = \left\{ \frac{205}{1496} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & 4x+\frac{7}{3} \\\Leftrightarrow & 15x+\frac{6}{11}& = & 4x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+18} & = & \color{red}{132x} +77 \\\Leftrightarrow & 495x \color{red}{+18} \color{blue}{-18} \color{blue}{-132x} & = & \color{red}{132x} +77 \color{blue}{-132x} \color{blue}{-18} \\\Leftrightarrow & 495x-132x& = & 77-18 \\\Leftrightarrow & \color{red}{363} x& = & 59 \\\Leftrightarrow & x = \frac{59}{363} & & \\ & V = \left\{ \frac{59}{363} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+12} & = & \color{red}{98x} +21 \\\Leftrightarrow & 210x \color{red}{+12} \color{blue}{-12} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{-12} \\\Leftrightarrow & 210x-98x& = & 21-12 \\\Leftrightarrow & \color{red}{112} x& = & 9 \\\Leftrightarrow & x = \frac{9}{112} & & \\ & V = \left\{ \frac{9}{112} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+63} & = & \color{red}{-140x} +50 \\\Leftrightarrow & 315x \color{red}{+63} \color{blue}{-63} \color{blue}{+140x} & = & \color{red}{-140x} +50 \color{blue}{+140x} \color{blue}{-63} \\\Leftrightarrow & 315x+140x& = & 50-63 \\\Leftrightarrow & \color{red}{455} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{455} & & \\\Leftrightarrow & x = \frac{-1}{35} & & \\ & V = \left\{ \frac{-1}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-176} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -1540x \color{red}{-176} \color{blue}{+176} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+176} \\\Leftrightarrow & -1540x+539x& = & 14+176 \\\Leftrightarrow & \color{red}{-1001} x& = & 190 \\\Leftrightarrow & x = \frac{190}{-1001} & & \\\Leftrightarrow & x = \frac{-190}{1001} & & \\ & V = \left\{ \frac{-190}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{3})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -6x+\frac{8}{3}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{105x} +27 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & -90x-105x& = & 27-40 \\\Leftrightarrow & \color{red}{-195} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-195} & & \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)