Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1980}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1980x \color{red}{-108} & = & \color{red}{462x} +55 \\\Leftrightarrow & -1980x \color{red}{-108} \color{blue}{+108} \color{blue}{-462x} & = & \color{red}{462x} +55 \color{blue}{-462x} \color{blue}{+108} \\\Leftrightarrow & -1980x-462x& = & 55+108 \\\Leftrightarrow & \color{red}{-2442} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-2442} & & \\\Leftrightarrow & x = \frac{-163}{2442} & & \\ & V = \left\{ \frac{-163}{2442} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -9x-\frac{6}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{-18} & = & \color{red}{-75x} +50 \\\Leftrightarrow & -135x \color{red}{-18} \color{blue}{+18} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+18} \\\Leftrightarrow & -135x+75x& = & 50+18 \\\Leftrightarrow & \color{red}{-60} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-60} & & \\\Leftrightarrow & x = \frac{-17}{15} & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 440x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{825} x& = & 162 \\\Leftrightarrow & x = \frac{162}{825} & & \\\Leftrightarrow & x = \frac{54}{275} & & \\ & V = \left\{ \frac{54}{275} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{7})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 12x-\frac{18}{7}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{180}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-180} & = & \color{red}{490x} +49 \\\Leftrightarrow & 840x \color{red}{-180} \color{blue}{+180} \color{blue}{-490x} & = & \color{red}{490x} +49 \color{blue}{-490x} \color{blue}{+180} \\\Leftrightarrow & 840x-490x& = & 49+180 \\\Leftrightarrow & \color{red}{350} x& = & 229 \\\Leftrightarrow & x = \frac{229}{350} & & \\ & V = \left\{ \frac{229}{350} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{9})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 8x-\frac{20}{9}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{288}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 288x \color{red}{-80} & = & \color{red}{252x} +15 \\\Leftrightarrow & 288x \color{red}{-80} \color{blue}{+80} \color{blue}{-252x} & = & \color{red}{252x} +15 \color{blue}{-252x} \color{blue}{+80} \\\Leftrightarrow & 288x-252x& = & 15+80 \\\Leftrightarrow & \color{red}{36} x& = & 95 \\\Leftrightarrow & x = \frac{95}{36} & & \\ & V = \left\{ \frac{95}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-70} & = & \color{red}{-120x} +12 \\\Leftrightarrow & -315x \color{red}{-70} \color{blue}{+70} \color{blue}{+120x} & = & \color{red}{-120x} +12 \color{blue}{+120x} \color{blue}{+70} \\\Leftrightarrow & -315x+120x& = & 12+70 \\\Leftrightarrow & \color{red}{-195} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-195} & & \\\Leftrightarrow & x = \frac{-82}{195} & & \\ & V = \left\{ \frac{-82}{195} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+56} & = & \color{red}{-147x} +18 \\\Leftrightarrow & -210x \color{red}{+56} \color{blue}{-56} \color{blue}{+147x} & = & \color{red}{-147x} +18 \color{blue}{+147x} \color{blue}{-56} \\\Leftrightarrow & -210x+147x& = & 18-56 \\\Leftrightarrow & \color{red}{-63} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-63} & & \\\Leftrightarrow & x = \frac{38}{63} & & \\ & V = \left\{ \frac{38}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{168}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 168x \color{red}{-36} & = & \color{red}{-294x} +49 \\\Leftrightarrow & 168x \color{red}{-36} \color{blue}{+36} \color{blue}{+294x} & = & \color{red}{-294x} +49 \color{blue}{+294x} \color{blue}{+36} \\\Leftrightarrow & 168x+294x& = & 49+36 \\\Leftrightarrow & \color{red}{462} x& = & 85 \\\Leftrightarrow & x = \frac{85}{462} & & \\ & V = \left\{ \frac{85}{462} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -15x-\frac{6}{11}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-12} & = & \color{red}{-176x} +55 \\\Leftrightarrow & -330x \color{red}{-12} \color{blue}{+12} \color{blue}{+176x} & = & \color{red}{-176x} +55 \color{blue}{+176x} \color{blue}{+12} \\\Leftrightarrow & -330x+176x& = & 55+12 \\\Leftrightarrow & \color{red}{-154} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-154} & & \\\Leftrightarrow & x = \frac{-67}{154} & & \\ & V = \left\{ \frac{-67}{154} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & -4x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-56} & = & \color{red}{-48x} +9 \\\Leftrightarrow & 252x \color{red}{-56} \color{blue}{+56} \color{blue}{+48x} & = & \color{red}{-48x} +9 \color{blue}{+48x} \color{blue}{+56} \\\Leftrightarrow & 252x+48x& = & 9+56 \\\Leftrightarrow & \color{red}{300} x& = & 65 \\\Leftrightarrow & x = \frac{65}{300} & & \\\Leftrightarrow & x = \frac{13}{60} & & \\ & V = \left\{ \frac{13}{60} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & 9x+\frac{3}{5} \\\Leftrightarrow & -28x+\frac{35}{3}& = & 9x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{175}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{135x} +9 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{-135x} & = & \color{red}{135x} +9 \color{blue}{-135x} \color{blue}{-175} \\\Leftrightarrow & -420x-135x& = & 9-175 \\\Leftrightarrow & \color{red}{-555} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-555} & & \\\Leftrightarrow & x = \frac{166}{555} & & \\ & V = \left\{ \frac{166}{555} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{8})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x-\frac{9}{8}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x- \frac{63}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{-63} & = & \color{red}{392x} +72 \\\Leftrightarrow & -336x \color{red}{-63} \color{blue}{+63} \color{blue}{-392x} & = & \color{red}{392x} +72 \color{blue}{-392x} \color{blue}{+63} \\\Leftrightarrow & -336x-392x& = & 72+63 \\\Leftrightarrow & \color{red}{-728} x& = & 135 \\\Leftrightarrow & x = \frac{135}{-728} & & \\\Leftrightarrow & x = \frac{-135}{728} & & \\ & V = \left\{ \frac{-135}{728} \right\} & \\\end{align}\)