Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{12})& = & -2x+\frac{4}{7} \\\Leftrightarrow & 15x+\frac{25}{12}& = & -2x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1260}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{-168}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1260x \color{red}{+175} & = & \color{red}{-168x} +48 \\\Leftrightarrow & 1260x \color{red}{+175} \color{blue}{-175} \color{blue}{+168x} & = & \color{red}{-168x} +48 \color{blue}{+168x} \color{blue}{-175} \\\Leftrightarrow & 1260x+168x& = & 48-175 \\\Leftrightarrow & \color{red}{1428} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1428} & & \\ & V = \left\{ \frac{-127}{1428} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{28}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-56} & = & \color{red}{-18x} +27 \\\Leftrightarrow & -84x \color{red}{-56} \color{blue}{+56} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{+56} \\\Leftrightarrow & -84x+18x& = & 27+56 \\\Leftrightarrow & \color{red}{-66} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-66} & & \\\Leftrightarrow & x = \frac{-83}{66} & & \\ & V = \left\{ \frac{-83}{66} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{245x} +25 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & 1050x-245x& = & 25-84 \\\Leftrightarrow & \color{red}{805} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{805} & & \\ & V = \left\{ \frac{-59}{805} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -4x+\frac{5}{7} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -4x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+168} & = & \color{red}{-140x} +25 \\\Leftrightarrow & -630x \color{red}{+168} \color{blue}{-168} \color{blue}{+140x} & = & \color{red}{-140x} +25 \color{blue}{+140x} \color{blue}{-168} \\\Leftrightarrow & -630x+140x& = & 25-168 \\\Leftrightarrow & \color{red}{-490} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{-490} & & \\\Leftrightarrow & x = \frac{143}{490} & & \\ & V = \left\{ \frac{143}{490} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+150} & = & \color{red}{275x} +77 \\\Leftrightarrow & -660x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +77 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & -660x-275x& = & 77-150 \\\Leftrightarrow & \color{red}{-935} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-935} & & \\\Leftrightarrow & x = \frac{73}{935} & & \\ & V = \left\{ \frac{73}{935} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+165} & = & \color{red}{-220x} +16 \\\Leftrightarrow & -528x \color{red}{+165} \color{blue}{-165} \color{blue}{+220x} & = & \color{red}{-220x} +16 \color{blue}{+220x} \color{blue}{-165} \\\Leftrightarrow & -528x+220x& = & 16-165 \\\Leftrightarrow & \color{red}{-308} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{-308} & & \\\Leftrightarrow & x = \frac{149}{308} & & \\ & V = \left\{ \frac{149}{308} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 9x+\frac{3}{8} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -352x \color{red}{+48} & = & \color{red}{792x} +33 \\\Leftrightarrow & -352x \color{red}{+48} \color{blue}{-48} \color{blue}{-792x} & = & \color{red}{792x} +33 \color{blue}{-792x} \color{blue}{-48} \\\Leftrightarrow & -352x-792x& = & 33-48 \\\Leftrightarrow & \color{red}{-1144} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-1144} & & \\\Leftrightarrow & x = \frac{15}{1144} & & \\ & V = \left\{ \frac{15}{1144} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & 4x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{20}{3}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{-200} & = & \color{red}{120x} +27 \\\Leftrightarrow & -450x \color{red}{-200} \color{blue}{+200} \color{blue}{-120x} & = & \color{red}{120x} +27 \color{blue}{-120x} \color{blue}{+200} \\\Leftrightarrow & -450x-120x& = & 27+200 \\\Leftrightarrow & \color{red}{-570} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-570} & & \\\Leftrightarrow & x = \frac{-227}{570} & & \\ & V = \left\{ \frac{-227}{570} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -14x-\frac{14}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-14} & = & \color{red}{9x} +2 \\\Leftrightarrow & -42x \color{red}{-14} \color{blue}{+14} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{+14} \\\Leftrightarrow & -42x-9x& = & 2+14 \\\Leftrightarrow & \color{red}{-51} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-51} & & \\\Leftrightarrow & x = \frac{-16}{51} & & \\ & V = \left\{ \frac{-16}{51} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-28} \\\Leftrightarrow & 252x+315x& = & 54-28 \\\Leftrightarrow & \color{red}{567} x& = & 26 \\\Leftrightarrow & x = \frac{26}{567} & & \\ & V = \left\{ \frac{26}{567} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+160} & = & \color{red}{350x} +63 \\\Leftrightarrow & -840x \color{red}{+160} \color{blue}{-160} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{-160} \\\Leftrightarrow & -840x-350x& = & 63-160 \\\Leftrightarrow & \color{red}{-1190} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1190} & & \\\Leftrightarrow & x = \frac{97}{1190} & & \\ & V = \left\{ \frac{97}{1190} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{11})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 8x+\frac{4}{11}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+4} & = & \color{red}{-99x} +2 \\\Leftrightarrow & 88x \color{red}{+4} \color{blue}{-4} \color{blue}{+99x} & = & \color{red}{-99x} +2 \color{blue}{+99x} \color{blue}{-4} \\\Leftrightarrow & 88x+99x& = & 2-4 \\\Leftrightarrow & \color{red}{187} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{187} & & \\ & V = \left\{ \frac{-2}{187} \right\} & \\\end{align}\)