Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-375}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -375x \color{red}{-100} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -375x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & -375x+105x& = & 18+100 \\\Leftrightarrow & \color{red}{-270} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-270} & & \\\Leftrightarrow & x = \frac{-59}{135} & & \\ & V = \left\{ \frac{-59}{135} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+12} & = & \color{red}{-28x} +21 \\\Leftrightarrow & 210x \color{red}{+12} \color{blue}{-12} \color{blue}{+28x} & = & \color{red}{-28x} +21 \color{blue}{+28x} \color{blue}{-12} \\\Leftrightarrow & 210x+28x& = & 21-12 \\\Leftrightarrow & \color{red}{238} x& = & 9 \\\Leftrightarrow & x = \frac{9}{238} & & \\ & V = \left\{ \frac{9}{238} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{-72} & = & \color{red}{210x} +35 \\\Leftrightarrow & -180x \color{red}{-72} \color{blue}{+72} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+72} \\\Leftrightarrow & -180x-210x& = & 35+72 \\\Leftrightarrow & \color{red}{-390} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-390} & & \\\Leftrightarrow & x = \frac{-107}{390} & & \\ & V = \left\{ \frac{-107}{390} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-54} & = & \color{red}{165x} +22 \\\Leftrightarrow & 396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & 396x-165x& = & 22+54 \\\Leftrightarrow & \color{red}{231} x& = & 76 \\\Leftrightarrow & x = \frac{76}{231} & & \\ & V = \left\{ \frac{76}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1260}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1260x \color{red}{+300} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -1260x \color{red}{+300} \color{blue}{-300} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-300} \\\Leftrightarrow & -1260x+350x& = & 63-300 \\\Leftrightarrow & \color{red}{-910} x& = & -237 \\\Leftrightarrow & x = \frac{-237}{-910} & & \\\Leftrightarrow & x = \frac{237}{910} & & \\ & V = \left\{ \frac{237}{910} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{15}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-135} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 945x \color{red}{-135} \color{blue}{+135} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+135} \\\Leftrightarrow & 945x+441x& = & 70+135 \\\Leftrightarrow & \color{red}{1386} x& = & 205 \\\Leftrightarrow & x = \frac{205}{1386} & & \\ & V = \left\{ \frac{205}{1386} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{2100}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 2100x \color{red}{-300} & = & \color{red}{490x} +21 \\\Leftrightarrow & 2100x \color{red}{-300} \color{blue}{+300} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+300} \\\Leftrightarrow & 2100x-490x& = & 21+300 \\\Leftrightarrow & \color{red}{1610} x& = & 321 \\\Leftrightarrow & x = \frac{321}{1610} & & \\ & V = \left\{ \frac{321}{1610} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{5})& = & -6x+\frac{8}{11} \\\Leftrightarrow & 35x-\frac{28}{5}& = & -6x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{-308} & = & \color{red}{-330x} +40 \\\Leftrightarrow & 1925x \color{red}{-308} \color{blue}{+308} \color{blue}{+330x} & = & \color{red}{-330x} +40 \color{blue}{+330x} \color{blue}{+308} \\\Leftrightarrow & 1925x+330x& = & 40+308 \\\Leftrightarrow & \color{red}{2255} x& = & 348 \\\Leftrightarrow & x = \frac{348}{2255} & & \\ & V = \left\{ \frac{348}{2255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+70} & = & \color{red}{-539x} +66 \\\Leftrightarrow & -770x \color{red}{+70} \color{blue}{-70} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-70} \\\Leftrightarrow & -770x+539x& = & 66-70 \\\Leftrightarrow & \color{red}{-231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-231} & & \\\Leftrightarrow & x = \frac{4}{231} & & \\ & V = \left\{ \frac{4}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+12} & = & \color{red}{70x} +49 \\\Leftrightarrow & 168x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & 168x-70x& = & 49-12 \\\Leftrightarrow & \color{red}{98} x& = & 37 \\\Leftrightarrow & x = \frac{37}{98} & & \\ & V = \left\{ \frac{37}{98} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{16}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x+ \frac{64}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{+64} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 352x \color{red}{+64} \color{blue}{-64} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-64} \\\Leftrightarrow & 352x+220x& = & 33-64 \\\Leftrightarrow & \color{red}{572} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{572} & & \\ & V = \left\{ \frac{-31}{572} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{4}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{12}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+12} \\\Leftrightarrow & 84x+189x& = & 70+12 \\\Leftrightarrow & \color{red}{273} x& = & 82 \\\Leftrightarrow & x = \frac{82}{273} & & \\ & V = \left\{ \frac{82}{273} \right\} & \\\end{align}\)