Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{11})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 14x+\frac{28}{11}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{308}{ \color{blue}{22} }x+ \frac{56}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 308x \color{red}{+56} & = & \color{red}{-198x} +99 \\\Leftrightarrow & 308x \color{red}{+56} \color{blue}{-56} \color{blue}{+198x} & = & \color{red}{-198x} +99 \color{blue}{+198x} \color{blue}{-56} \\\Leftrightarrow & 308x+198x& = & 99-56 \\\Leftrightarrow & \color{red}{506} x& = & 43 \\\Leftrightarrow & x = \frac{43}{506} & & \\ & V = \left\{ \frac{43}{506} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -18x+\frac{24}{5}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+216} & = & \color{red}{225x} +50 \\\Leftrightarrow & -810x \color{red}{+216} \color{blue}{-216} \color{blue}{-225x} & = & \color{red}{225x} +50 \color{blue}{-225x} \color{blue}{-216} \\\Leftrightarrow & -810x-225x& = & 50-216 \\\Leftrightarrow & \color{red}{-1035} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-1035} & & \\\Leftrightarrow & x = \frac{166}{1035} & & \\ & V = \left\{ \frac{166}{1035} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{4})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-45} & = & \color{red}{84x} +40 \\\Leftrightarrow & -120x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +40 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -120x-84x& = & 40+45 \\\Leftrightarrow & \color{red}{-204} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-204} & & \\\Leftrightarrow & x = \frac{-5}{12} & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 30x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{5} x& = & 18 \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -28x+\frac{35}{3}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+385} & = & \color{red}{-99x} +12 \\\Leftrightarrow & -924x \color{red}{+385} \color{blue}{-385} \color{blue}{+99x} & = & \color{red}{-99x} +12 \color{blue}{+99x} \color{blue}{-385} \\\Leftrightarrow & -924x+99x& = & 12-385 \\\Leftrightarrow & \color{red}{-825} x& = & -373 \\\Leftrightarrow & x = \frac{-373}{-825} & & \\\Leftrightarrow & x = \frac{373}{825} & & \\ & V = \left\{ \frac{373}{825} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+162} & = & \color{red}{693x} +110 \\\Leftrightarrow & -2970x \color{red}{+162} \color{blue}{-162} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-162} \\\Leftrightarrow & -2970x-693x& = & 110-162 \\\Leftrightarrow & \color{red}{-3663} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-3663} & & \\\Leftrightarrow & x = \frac{52}{3663} & & \\ & V = \left\{ \frac{52}{3663} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+66} & = & \color{red}{-385x} +21 \\\Leftrightarrow & 924x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +21 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & 924x+385x& = & 21-66 \\\Leftrightarrow & \color{red}{1309} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{1309} & & \\ & V = \left\{ \frac{-45}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & -240x+100x& = & 45-48 \\\Leftrightarrow & \color{red}{-140} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-140} & & \\\Leftrightarrow & x = \frac{3}{140} & & \\ & V = \left\{ \frac{3}{140} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{8})& = & 2x+\frac{4}{9} \\\Leftrightarrow & 21x-\frac{35}{8}& = & 2x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1512}{ \color{blue}{72} }x- \frac{315}{ \color{blue}{72} })& = & (\frac{144}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1512x \color{red}{-315} & = & \color{red}{144x} +32 \\\Leftrightarrow & 1512x \color{red}{-315} \color{blue}{+315} \color{blue}{-144x} & = & \color{red}{144x} +32 \color{blue}{-144x} \color{blue}{+315} \\\Leftrightarrow & 1512x-144x& = & 32+315 \\\Leftrightarrow & \color{red}{1368} x& = & 347 \\\Leftrightarrow & x = \frac{347}{1368} & & \\ & V = \left\{ \frac{347}{1368} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & 3x+\frac{5}{8} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{-64} & = & \color{red}{72x} +15 \\\Leftrightarrow & 192x \color{red}{-64} \color{blue}{+64} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{+64} \\\Leftrightarrow & 192x-72x& = & 15+64 \\\Leftrightarrow & \color{red}{120} x& = & 79 \\\Leftrightarrow & x = \frac{79}{120} & & \\ & V = \left\{ \frac{79}{120} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{11})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -21x-\frac{35}{11}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-105} & = & \color{red}{-264x} +110 \\\Leftrightarrow & -693x \color{red}{-105} \color{blue}{+105} \color{blue}{+264x} & = & \color{red}{-264x} +110 \color{blue}{+264x} \color{blue}{+105} \\\Leftrightarrow & -693x+264x& = & 110+105 \\\Leftrightarrow & \color{red}{-429} x& = & 215 \\\Leftrightarrow & x = \frac{215}{-429} & & \\\Leftrightarrow & x = \frac{-215}{429} & & \\ & V = \left\{ \frac{-215}{429} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{6})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -35x-\frac{35}{6}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{-175} & = & \color{red}{-270x} +9 \\\Leftrightarrow & -1050x \color{red}{-175} \color{blue}{+175} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{+175} \\\Leftrightarrow & -1050x+270x& = & 9+175 \\\Leftrightarrow & \color{red}{-780} x& = & 184 \\\Leftrightarrow & x = \frac{184}{-780} & & \\\Leftrightarrow & x = \frac{-46}{195} & & \\ & V = \left\{ \frac{-46}{195} \right\} & \\\end{align}\)