Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{8})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 25x+\frac{15}{8}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{200}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 200x \color{red}{+15} & = & \color{red}{-24x} +3 \\\Leftrightarrow & 200x \color{red}{+15} \color{blue}{-15} \color{blue}{+24x} & = & \color{red}{-24x} +3 \color{blue}{+24x} \color{blue}{-15} \\\Leftrightarrow & 200x+24x& = & 3-15 \\\Leftrightarrow & \color{red}{224} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{224} & & \\\Leftrightarrow & x = \frac{-3}{56} & & \\ & V = \left\{ \frac{-3}{56} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & -4x+\frac{3}{7} \\\Leftrightarrow & 21x+\frac{28}{9}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{+196} & = & \color{red}{-252x} +27 \\\Leftrightarrow & 1323x \color{red}{+196} \color{blue}{-196} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{-196} \\\Leftrightarrow & 1323x+252x& = & 27-196 \\\Leftrightarrow & \color{red}{1575} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{1575} & & \\ & V = \left\{ \frac{-169}{1575} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+75} & = & \color{red}{-100x} +6 \\\Leftrightarrow & -240x \color{red}{+75} \color{blue}{-75} \color{blue}{+100x} & = & \color{red}{-100x} +6 \color{blue}{+100x} \color{blue}{-75} \\\Leftrightarrow & -240x+100x& = & 6-75 \\\Leftrightarrow & \color{red}{-140} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-140} & & \\\Leftrightarrow & x = \frac{69}{140} & & \\ & V = \left\{ \frac{69}{140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & 2x+\frac{5}{2} \\\Leftrightarrow & 21x-\frac{35}{3}& = & 2x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-70} & = & \color{red}{12x} +15 \\\Leftrightarrow & 126x \color{red}{-70} \color{blue}{+70} \color{blue}{-12x} & = & \color{red}{12x} +15 \color{blue}{-12x} \color{blue}{+70} \\\Leftrightarrow & 126x-12x& = & 15+70 \\\Leftrightarrow & \color{red}{114} x& = & 85 \\\Leftrightarrow & x = \frac{85}{114} & & \\ & V = \left\{ \frac{85}{114} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-40} & = & \color{red}{315x} +72 \\\Leftrightarrow & -450x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -450x-315x& = & 72+40 \\\Leftrightarrow & \color{red}{-765} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-765} & & \\\Leftrightarrow & x = \frac{-112}{765} & & \\ & V = \left\{ \frac{-112}{765} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{240}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-240} & = & \color{red}{440x} +99 \\\Leftrightarrow & -1056x \color{red}{-240} \color{blue}{+240} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{+240} \\\Leftrightarrow & -1056x-440x& = & 99+240 \\\Leftrightarrow & \color{red}{-1496} x& = & 339 \\\Leftrightarrow & x = \frac{339}{-1496} & & \\\Leftrightarrow & x = \frac{-339}{1496} & & \\ & V = \left\{ \frac{-339}{1496} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{15}{2}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{-50x} +12 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{+50x} & = & \color{red}{-50x} +12 \color{blue}{+50x} \color{blue}{-75} \\\Leftrightarrow & -120x+50x& = & 12-75 \\\Leftrightarrow & \color{red}{-70} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-70} & & \\\Leftrightarrow & x = \frac{9}{10} & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -20x-\frac{15}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-135} & = & \color{red}{693x} +55 \\\Leftrightarrow & -1980x \color{red}{-135} \color{blue}{+135} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{+135} \\\Leftrightarrow & -1980x-693x& = & 55+135 \\\Leftrightarrow & \color{red}{-2673} x& = & 190 \\\Leftrightarrow & x = \frac{190}{-2673} & & \\\Leftrightarrow & x = \frac{-190}{2673} & & \\ & V = \left\{ \frac{-190}{2673} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+176} & = & \color{red}{-165x} +18 \\\Leftrightarrow & -396x \color{red}{+176} \color{blue}{-176} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{-176} \\\Leftrightarrow & -396x+165x& = & 18-176 \\\Leftrightarrow & \color{red}{-231} x& = & -158 \\\Leftrightarrow & x = \frac{-158}{-231} & & \\\Leftrightarrow & x = \frac{158}{231} & & \\ & V = \left\{ \frac{158}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{63x} +5 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -90x-63x& = & 5+8 \\\Leftrightarrow & \color{red}{-153} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-153} & & \\\Leftrightarrow & x = \frac{-13}{153} & & \\ & V = \left\{ \frac{-13}{153} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{-60x} +9 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{-56} \\\Leftrightarrow & -168x+60x& = & 9-56 \\\Leftrightarrow & \color{red}{-108} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-108} & & \\\Leftrightarrow & x = \frac{47}{108} & & \\ & V = \left\{ \frac{47}{108} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{14}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+154} & = & \color{red}{-297x} +54 \\\Leftrightarrow & -1386x \color{red}{+154} \color{blue}{-154} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-154} \\\Leftrightarrow & -1386x+297x& = & 54-154 \\\Leftrightarrow & \color{red}{-1089} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-1089} & & \\\Leftrightarrow & x = \frac{100}{1089} & & \\ & V = \left\{ \frac{100}{1089} \right\} & \\\end{align}\)