Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{8})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x-\frac{35}{8}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{320x} +16 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{-320x} & = & \color{red}{320x} +16 \color{blue}{-320x} \color{blue}{+175} \\\Leftrightarrow & -840x-320x& = & 16+175 \\\Leftrightarrow & \color{red}{-1160} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-1160} & & \\\Leftrightarrow & x = \frac{-191}{1160} & & \\ & V = \left\{ \frac{-191}{1160} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{55x} +7 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -264x-55x& = & 7-18 \\\Leftrightarrow & \color{red}{-319} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-319} & & \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{10})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{9}{10}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{20}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-99} & = & \color{red}{550x} +20 \\\Leftrightarrow & -1320x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +20 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & -1320x-550x& = & 20+99 \\\Leftrightarrow & \color{red}{-1870} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-1870} & & \\\Leftrightarrow & x = \frac{-7}{110} & & \\ & V = \left\{ \frac{-7}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-154} & = & \color{red}{264x} +30 \\\Leftrightarrow & -693x \color{red}{-154} \color{blue}{+154} \color{blue}{-264x} & = & \color{red}{264x} +30 \color{blue}{-264x} \color{blue}{+154} \\\Leftrightarrow & -693x-264x& = & 30+154 \\\Leftrightarrow & \color{red}{-957} x& = & 184 \\\Leftrightarrow & x = \frac{184}{-957} & & \\\Leftrightarrow & x = \frac{-184}{957} & & \\ & V = \left\{ \frac{-184}{957} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{81x} +12 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +12 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -36x-81x& = & 12-8 \\\Leftrightarrow & \color{red}{-117} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-117} & & \\\Leftrightarrow & x = \frac{-4}{117} & & \\ & V = \left\{ \frac{-4}{117} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 14x+\frac{35}{6}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{924}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{198}{ \color{blue}{66} }x+ \frac{30}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 924x \color{red}{+385} & = & \color{red}{198x} +30 \\\Leftrightarrow & 924x \color{red}{+385} \color{blue}{-385} \color{blue}{-198x} & = & \color{red}{198x} +30 \color{blue}{-198x} \color{blue}{-385} \\\Leftrightarrow & 924x-198x& = & 30-385 \\\Leftrightarrow & \color{red}{726} x& = & -355 \\\Leftrightarrow & x = \frac{-355}{726} & & \\ & V = \left\{ \frac{-355}{726} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-40} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 60x \color{red}{-40} \color{blue}{+40} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+40} \\\Leftrightarrow & 60x+75x& = & 18+40 \\\Leftrightarrow & \color{red}{135} x& = & 58 \\\Leftrightarrow & x = \frac{58}{135} & & \\ & V = \left\{ \frac{58}{135} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & -4x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{-40x} +45 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{+40x} & = & \color{red}{-40x} +45 \color{blue}{+40x} \color{blue}{-24} \\\Leftrightarrow & -150x+40x& = & 45-24 \\\Leftrightarrow & \color{red}{-110} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-110} & & \\\Leftrightarrow & x = \frac{-21}{110} & & \\ & V = \left\{ \frac{-21}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -6x+\frac{4}{5} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -6x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{-90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-140} & = & \color{red}{-90x} +12 \\\Leftrightarrow & 525x \color{red}{-140} \color{blue}{+140} \color{blue}{+90x} & = & \color{red}{-90x} +12 \color{blue}{+90x} \color{blue}{+140} \\\Leftrightarrow & 525x+90x& = & 12+140 \\\Leftrightarrow & \color{red}{615} x& = & 152 \\\Leftrightarrow & x = \frac{152}{615} & & \\ & V = \left\{ \frac{152}{615} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-48}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -48x \color{red}{-15} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -48x \color{red}{-15} \color{blue}{+15} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{+15} \\\Leftrightarrow & -48x+20x& = & 9+15 \\\Leftrightarrow & \color{red}{-28} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-28} & & \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 15x-\frac{12}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-48} & = & \color{red}{196x} +63 \\\Leftrightarrow & 420x \color{red}{-48} \color{blue}{+48} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+48} \\\Leftrightarrow & 420x-196x& = & 63+48 \\\Leftrightarrow & \color{red}{224} x& = & 111 \\\Leftrightarrow & x = \frac{111}{224} & & \\ & V = \left\{ \frac{111}{224} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{2})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -25x-\frac{25}{2}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-75} & = & \color{red}{18x} +5 \\\Leftrightarrow & -150x \color{red}{-75} \color{blue}{+75} \color{blue}{-18x} & = & \color{red}{18x} +5 \color{blue}{-18x} \color{blue}{+75} \\\Leftrightarrow & -150x-18x& = & 5+75 \\\Leftrightarrow & \color{red}{-168} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-168} & & \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)