Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{6})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -35x+\frac{35}{6}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+35} & = & \color{red}{-54x} +5 \\\Leftrightarrow & -210x \color{red}{+35} \color{blue}{-35} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-35} \\\Leftrightarrow & -210x+54x& = & 5-35 \\\Leftrightarrow & \color{red}{-156} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{-156} & & \\\Leftrightarrow & x = \frac{5}{26} & & \\ & V = \left\{ \frac{5}{26} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & -3x+\frac{7}{12} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{-36x} +7 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{+36x} & = & \color{red}{-36x} +7 \color{blue}{+36x} \color{blue}{-140} \\\Leftrightarrow & -420x+36x& = & 7-140 \\\Leftrightarrow & \color{red}{-384} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-384} & & \\\Leftrightarrow & x = \frac{133}{384} & & \\ & V = \left\{ \frac{133}{384} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 4x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{60x} +40 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{-36} \\\Leftrightarrow & 225x-60x& = & 40-36 \\\Leftrightarrow & \color{red}{165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{165} & & \\ & V = \left\{ \frac{4}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -8x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -8x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{-80} & = & \color{red}{-448x} +49 \\\Leftrightarrow & 840x \color{red}{-80} \color{blue}{+80} \color{blue}{+448x} & = & \color{red}{-448x} +49 \color{blue}{+448x} \color{blue}{+80} \\\Leftrightarrow & 840x+448x& = & 49+80 \\\Leftrightarrow & \color{red}{1288} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1288} & & \\ & V = \left\{ \frac{129}{1288} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+96} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 528x \color{red}{+96} \color{blue}{-96} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-96} \\\Leftrightarrow & 528x+220x& = & 33-96 \\\Leftrightarrow & \color{red}{748} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{748} & & \\ & V = \left\{ \frac{-63}{748} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{-150x} +36 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{+150x} & = & \color{red}{-150x} +36 \color{blue}{+150x} \color{blue}{+175} \\\Leftrightarrow & 420x+150x& = & 36+175 \\\Leftrightarrow & \color{red}{570} x& = & 211 \\\Leftrightarrow & x = \frac{211}{570} & & \\ & V = \left\{ \frac{211}{570} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{9})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 6x+\frac{4}{9}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+28} & = & \color{red}{315x} +54 \\\Leftrightarrow & 378x \color{red}{+28} \color{blue}{-28} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-28} \\\Leftrightarrow & 378x-315x& = & 54-28 \\\Leftrightarrow & \color{red}{63} x& = & 26 \\\Leftrightarrow & x = \frac{26}{63} & & \\ & V = \left\{ \frac{26}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{11})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -24x-\frac{12}{11}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-36} & = & \color{red}{165x} +77 \\\Leftrightarrow & -792x \color{red}{-36} \color{blue}{+36} \color{blue}{-165x} & = & \color{red}{165x} +77 \color{blue}{-165x} \color{blue}{+36} \\\Leftrightarrow & -792x-165x& = & 77+36 \\\Leftrightarrow & \color{red}{-957} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-957} & & \\\Leftrightarrow & x = \frac{-113}{957} & & \\ & V = \left\{ \frac{-113}{957} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{35}{11}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x- \frac{70}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{-70} & = & \color{red}{-66x} +33 \\\Leftrightarrow & 616x \color{red}{-70} \color{blue}{+70} \color{blue}{+66x} & = & \color{red}{-66x} +33 \color{blue}{+66x} \color{blue}{+70} \\\Leftrightarrow & 616x+66x& = & 33+70 \\\Leftrightarrow & \color{red}{682} x& = & 103 \\\Leftrightarrow & x = \frac{103}{682} & & \\ & V = \left\{ \frac{103}{682} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-12} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -40x \color{red}{-12} \color{blue}{+12} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+12} \\\Leftrightarrow & -40x+45x& = & 6+12 \\\Leftrightarrow & \color{red}{5} x& = & 18 \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{96x} +80 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{-96x} & = & \color{red}{96x} +80 \color{blue}{-96x} \color{blue}{-63} \\\Leftrightarrow & 504x-96x& = & 80-63 \\\Leftrightarrow & \color{red}{408} x& = & 17 \\\Leftrightarrow & x = \frac{17}{408} & & \\\Leftrightarrow & x = \frac{1}{24} & & \\ & V = \left\{ \frac{1}{24} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{-90} & = & \color{red}{-567x} +56 \\\Leftrightarrow & -252x \color{red}{-90} \color{blue}{+90} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{+90} \\\Leftrightarrow & -252x+567x& = & 56+90 \\\Leftrightarrow & \color{red}{315} x& = & 146 \\\Leftrightarrow & x = \frac{146}{315} & & \\ & V = \left\{ \frac{146}{315} \right\} & \\\end{align}\)