Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{6}{11}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-12} & = & \color{red}{-88x} +33 \\\Leftrightarrow & -330x \color{red}{-12} \color{blue}{+12} \color{blue}{+88x} & = & \color{red}{-88x} +33 \color{blue}{+88x} \color{blue}{+12} \\\Leftrightarrow & -330x+88x& = & 33+12 \\\Leftrightarrow & \color{red}{-242} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-242} & & \\\Leftrightarrow & x = \frac{-45}{242} & & \\ & V = \left\{ \frac{-45}{242} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{440}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 440x \color{red}{-100} & = & \color{red}{990x} +99 \\\Leftrightarrow & 440x \color{red}{-100} \color{blue}{+100} \color{blue}{-990x} & = & \color{red}{990x} +99 \color{blue}{-990x} \color{blue}{+100} \\\Leftrightarrow & 440x-990x& = & 99+100 \\\Leftrightarrow & \color{red}{-550} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-550} & & \\\Leftrightarrow & x = \frac{-199}{550} & & \\ & V = \left\{ \frac{-199}{550} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+162} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 1188x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & 1188x+495x& = & 88-162 \\\Leftrightarrow & \color{red}{1683} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1683} & & \\ & V = \left\{ \frac{-74}{1683} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{8})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 28x+\frac{35}{8}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x+ \frac{385}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{+385} & = & \color{red}{264x} +32 \\\Leftrightarrow & 2464x \color{red}{+385} \color{blue}{-385} \color{blue}{-264x} & = & \color{red}{264x} +32 \color{blue}{-264x} \color{blue}{-385} \\\Leftrightarrow & 2464x-264x& = & 32-385 \\\Leftrightarrow & \color{red}{2200} x& = & -353 \\\Leftrightarrow & x = \frac{-353}{2200} & & \\ & V = \left\{ \frac{-353}{2200} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{10}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+10} & = & \color{red}{9x} +8 \\\Leftrightarrow & -24x \color{red}{+10} \color{blue}{-10} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{-10} \\\Leftrightarrow & -24x-9x& = & 8-10 \\\Leftrightarrow & \color{red}{-33} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-33} & & \\\Leftrightarrow & x = \frac{2}{33} & & \\ & V = \left\{ \frac{2}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{9})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{28}{9}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{-81x} +12 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{+81x} & = & \color{red}{-81x} +12 \color{blue}{+81x} \color{blue}{+28} \\\Leftrightarrow & 126x+81x& = & 12+28 \\\Leftrightarrow & \color{red}{207} x& = & 40 \\\Leftrightarrow & x = \frac{40}{207} & & \\ & V = \left\{ \frac{40}{207} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{12})& = & 4x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{35}{12}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1260}{ \color{blue}{60} }x- \frac{175}{ \color{blue}{60} })& = & (\frac{240}{ \color{blue}{60} }x+ \frac{24}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1260x \color{red}{-175} & = & \color{red}{240x} +24 \\\Leftrightarrow & 1260x \color{red}{-175} \color{blue}{+175} \color{blue}{-240x} & = & \color{red}{240x} +24 \color{blue}{-240x} \color{blue}{+175} \\\Leftrightarrow & 1260x-240x& = & 24+175 \\\Leftrightarrow & \color{red}{1020} x& = & 199 \\\Leftrightarrow & x = \frac{199}{1020} & & \\ & V = \left\{ \frac{199}{1020} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{9})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{14}{9}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-14} & = & \color{red}{-81x} +12 \\\Leftrightarrow & -252x \color{red}{-14} \color{blue}{+14} \color{blue}{+81x} & = & \color{red}{-81x} +12 \color{blue}{+81x} \color{blue}{+14} \\\Leftrightarrow & -252x+81x& = & 12+14 \\\Leftrightarrow & \color{red}{-171} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-171} & & \\\Leftrightarrow & x = \frac{-26}{171} & & \\ & V = \left\{ \frac{-26}{171} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{-147x} +49 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{+147x} & = & \color{red}{-147x} +49 \color{blue}{+147x} \color{blue}{-18} \\\Leftrightarrow & 168x+147x& = & 49-18 \\\Leftrightarrow & \color{red}{315} x& = & 31 \\\Leftrightarrow & x = \frac{31}{315} & & \\ & V = \left\{ \frac{31}{315} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -28x-\frac{35}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x- \frac{140}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{-140} & = & \color{red}{220x} +33 \\\Leftrightarrow & -1232x \color{red}{-140} \color{blue}{+140} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+140} \\\Leftrightarrow & -1232x-220x& = & 33+140 \\\Leftrightarrow & \color{red}{-1452} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-1452} & & \\\Leftrightarrow & x = \frac{-173}{1452} & & \\ & V = \left\{ \frac{-173}{1452} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{3})& = & -7x+\frac{3}{11} \\\Leftrightarrow & 6x+\frac{4}{3}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+44} & = & \color{red}{-231x} +9 \\\Leftrightarrow & 198x \color{red}{+44} \color{blue}{-44} \color{blue}{+231x} & = & \color{red}{-231x} +9 \color{blue}{+231x} \color{blue}{-44} \\\Leftrightarrow & 198x+231x& = & 9-44 \\\Leftrightarrow & \color{red}{429} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{429} & & \\ & V = \left\{ \frac{-35}{429} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{5})& = & 6x+\frac{8}{9} \\\Leftrightarrow & -28x-\frac{28}{5}& = & 6x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{252}{ \color{blue}{45} })& = & (\frac{270}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-252} & = & \color{red}{270x} +40 \\\Leftrightarrow & -1260x \color{red}{-252} \color{blue}{+252} \color{blue}{-270x} & = & \color{red}{270x} +40 \color{blue}{-270x} \color{blue}{+252} \\\Leftrightarrow & -1260x-270x& = & 40+252 \\\Leftrightarrow & \color{red}{-1530} x& = & 292 \\\Leftrightarrow & x = \frac{292}{-1530} & & \\\Leftrightarrow & x = \frac{-146}{765} & & \\ & V = \left\{ \frac{-146}{765} \right\} & \\\end{align}\)