Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{-70x} +49 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{-60} \\\Leftrightarrow & 252x+70x& = & 49-60 \\\Leftrightarrow & \color{red}{322} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{322} & & \\ & V = \left\{ \frac{-11}{322} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & -6x+\frac{9}{4} \\\Leftrightarrow & 25x-\frac{10}{11}& = & -6x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-264}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-40} & = & \color{red}{-264x} +99 \\\Leftrightarrow & 1100x \color{red}{-40} \color{blue}{+40} \color{blue}{+264x} & = & \color{red}{-264x} +99 \color{blue}{+264x} \color{blue}{+40} \\\Leftrightarrow & 1100x+264x& = & 99+40 \\\Leftrightarrow & \color{red}{1364} x& = & 139 \\\Leftrightarrow & x = \frac{139}{1364} & & \\ & V = \left\{ \frac{139}{1364} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{5})& = & 2x+\frac{5}{9} \\\Leftrightarrow & 15x-\frac{9}{5}& = & 2x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{-81} & = & \color{red}{90x} +25 \\\Leftrightarrow & 675x \color{red}{-81} \color{blue}{+81} \color{blue}{-90x} & = & \color{red}{90x} +25 \color{blue}{-90x} \color{blue}{+81} \\\Leftrightarrow & 675x-90x& = & 25+81 \\\Leftrightarrow & \color{red}{585} x& = & 106 \\\Leftrightarrow & x = \frac{106}{585} & & \\ & V = \left\{ \frac{106}{585} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{11})& = & -4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-45} & = & \color{red}{-132x} +110 \\\Leftrightarrow & -495x \color{red}{-45} \color{blue}{+45} \color{blue}{+132x} & = & \color{red}{-132x} +110 \color{blue}{+132x} \color{blue}{+45} \\\Leftrightarrow & -495x+132x& = & 110+45 \\\Leftrightarrow & \color{red}{-363} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-363} & & \\\Leftrightarrow & x = \frac{-155}{363} & & \\ & V = \left\{ \frac{-155}{363} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{11})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 28x+\frac{21}{11}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+147} & = & \color{red}{-231x} +66 \\\Leftrightarrow & 2156x \color{red}{+147} \color{blue}{-147} \color{blue}{+231x} & = & \color{red}{-231x} +66 \color{blue}{+231x} \color{blue}{-147} \\\Leftrightarrow & 2156x+231x& = & 66-147 \\\Leftrightarrow & \color{red}{2387} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{2387} & & \\ & V = \left\{ \frac{-81}{2387} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{-63x} +9 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{-20} \\\Leftrightarrow & 140x+63x& = & 9-20 \\\Leftrightarrow & \color{red}{203} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{203} & & \\ & V = \left\{ \frac{-11}{203} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{75x} +21 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{-75x} & = & \color{red}{75x} +21 \color{blue}{-75x} \color{blue}{-70} \\\Leftrightarrow & 315x-75x& = & 21-70 \\\Leftrightarrow & \color{red}{240} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{240} & & \\ & V = \left\{ \frac{-49}{240} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{18x} +9 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+35} \\\Leftrightarrow & 84x-18x& = & 9+35 \\\Leftrightarrow & \color{red}{66} x& = & 44 \\\Leftrightarrow & x = \frac{44}{66} & & \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -28x+\frac{21}{4}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-112}{ \color{blue}{4} }x+ \frac{21}{ \color{blue}{4} })& = & (\frac{-36}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -112x \color{red}{+21} & = & \color{red}{-36x} +6 \\\Leftrightarrow & -112x \color{red}{+21} \color{blue}{-21} \color{blue}{+36x} & = & \color{red}{-36x} +6 \color{blue}{+36x} \color{blue}{-21} \\\Leftrightarrow & -112x+36x& = & 6-21 \\\Leftrightarrow & \color{red}{-76} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-76} & & \\\Leftrightarrow & x = \frac{15}{76} & & \\ & V = \left\{ \frac{15}{76} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-70} & = & \color{red}{-539x} +55 \\\Leftrightarrow & -462x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & -462x+539x& = & 55+70 \\\Leftrightarrow & \color{red}{77} x& = & 125 \\\Leftrightarrow & x = \frac{125}{77} & & \\ & V = \left\{ \frac{125}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{+16} & = & \color{red}{90x} +45 \\\Leftrightarrow & -216x \color{red}{+16} \color{blue}{-16} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{-16} \\\Leftrightarrow & -216x-90x& = & 45-16 \\\Leftrightarrow & \color{red}{-306} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-306} & & \\\Leftrightarrow & x = \frac{-29}{306} & & \\ & V = \left\{ \frac{-29}{306} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{105x} +40 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 90x-105x& = & 40+18 \\\Leftrightarrow & \color{red}{-15} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-15} & & \\\Leftrightarrow & x = \frac{-58}{15} & & \\ & V = \left\{ \frac{-58}{15} \right\} & \\\end{align}\)