Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{11})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 10x+\frac{25}{11}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+125} & = & \color{red}{495x} +22 \\\Leftrightarrow & 550x \color{red}{+125} \color{blue}{-125} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{-125} \\\Leftrightarrow & 550x-495x& = & 22-125 \\\Leftrightarrow & \color{red}{55} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{55} & & \\ & V = \left\{ \frac{-103}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{16}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+48} & = & \color{red}{165x} +88 \\\Leftrightarrow & 396x \color{red}{+48} \color{blue}{-48} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{-48} \\\Leftrightarrow & 396x-165x& = & 88-48 \\\Leftrightarrow & \color{red}{231} x& = & 40 \\\Leftrightarrow & x = \frac{40}{231} & & \\ & V = \left\{ \frac{40}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-264} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 660x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & 660x+275x& = & 30+264 \\\Leftrightarrow & \color{red}{935} x& = & 294 \\\Leftrightarrow & x = \frac{294}{935} & & \\ & V = \left\{ \frac{294}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{150x} +36 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-150x} & = & \color{red}{150x} +36 \color{blue}{-150x} \color{blue}{+175} \\\Leftrightarrow & 420x-150x& = & 36+175 \\\Leftrightarrow & \color{red}{270} x& = & 211 \\\Leftrightarrow & x = \frac{211}{270} & & \\ & V = \left\{ \frac{211}{270} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-448}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -448x \color{red}{-80} & = & \color{red}{-196x} +63 \\\Leftrightarrow & -448x \color{red}{-80} \color{blue}{+80} \color{blue}{+196x} & = & \color{red}{-196x} +63 \color{blue}{+196x} \color{blue}{+80} \\\Leftrightarrow & -448x+196x& = & 63+80 \\\Leftrightarrow & \color{red}{-252} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-252} & & \\\Leftrightarrow & x = \frac{-143}{252} & & \\ & V = \left\{ \frac{-143}{252} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 28x+\frac{14}{9}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x+ \frac{70}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{+70} & = & \color{red}{-225x} +63 \\\Leftrightarrow & 1260x \color{red}{+70} \color{blue}{-70} \color{blue}{+225x} & = & \color{red}{-225x} +63 \color{blue}{+225x} \color{blue}{-70} \\\Leftrightarrow & 1260x+225x& = & 63-70 \\\Leftrightarrow & \color{red}{1485} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{1485} & & \\ & V = \left\{ \frac{-7}{1485} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-6} & = & \color{red}{35x} +4 \\\Leftrightarrow & -28x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -28x-35x& = & 4+6 \\\Leftrightarrow & \color{red}{-63} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-63} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{160x} +48 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{-160x} & = & \color{red}{160x} +48 \color{blue}{-160x} \color{blue}{+105} \\\Leftrightarrow & 840x-160x& = & 48+105 \\\Leftrightarrow & \color{red}{680} x& = & 153 \\\Leftrightarrow & x = \frac{153}{680} & & \\\Leftrightarrow & x = \frac{9}{40} & & \\ & V = \left\{ \frac{9}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+96} & = & \color{red}{360x} +15 \\\Leftrightarrow & -320x \color{red}{+96} \color{blue}{-96} \color{blue}{-360x} & = & \color{red}{360x} +15 \color{blue}{-360x} \color{blue}{-96} \\\Leftrightarrow & -320x-360x& = & 15-96 \\\Leftrightarrow & \color{red}{-680} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-680} & & \\\Leftrightarrow & x = \frac{81}{680} & & \\ & V = \left\{ \frac{81}{680} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{-294x} +35 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{-180} \\\Leftrightarrow & 1260x+294x& = & 35-180 \\\Leftrightarrow & \color{red}{1554} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{1554} & & \\ & V = \left\{ \frac{-145}{1554} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{7})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{24}{7}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{240}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-240} & = & \color{red}{-350x} +49 \\\Leftrightarrow & -840x \color{red}{-240} \color{blue}{+240} \color{blue}{+350x} & = & \color{red}{-350x} +49 \color{blue}{+350x} \color{blue}{+240} \\\Leftrightarrow & -840x+350x& = & 49+240 \\\Leftrightarrow & \color{red}{-490} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-490} & & \\\Leftrightarrow & x = \frac{-289}{490} & & \\ & V = \left\{ \frac{-289}{490} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{9})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{16}{9}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+16} & = & \color{red}{27x} +2 \\\Leftrightarrow & 180x \color{red}{+16} \color{blue}{-16} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{-16} \\\Leftrightarrow & 180x-27x& = & 2-16 \\\Leftrightarrow & \color{red}{153} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{153} & & \\ & V = \left\{ \frac{-14}{153} \right\} & \\\end{align}\)