Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{8}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-8} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -30x \color{red}{-8} \color{blue}{+8} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+8} \\\Leftrightarrow & -30x+35x& = & 6+8 \\\Leftrightarrow & \color{red}{5} x& = & 14 \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-24} & = & \color{red}{-110x} +77 \\\Leftrightarrow & 264x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & 264x+110x& = & 77+24 \\\Leftrightarrow & \color{red}{374} x& = & 101 \\\Leftrightarrow & x = \frac{101}{374} & & \\ & V = \left\{ \frac{101}{374} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+30} & = & \color{red}{55x} +10 \\\Leftrightarrow & -132x \color{red}{+30} \color{blue}{-30} \color{blue}{-55x} & = & \color{red}{55x} +10 \color{blue}{-55x} \color{blue}{-30} \\\Leftrightarrow & -132x-55x& = & 10-30 \\\Leftrightarrow & \color{red}{-187} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-187} & & \\\Leftrightarrow & x = \frac{20}{187} & & \\ & V = \left\{ \frac{20}{187} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{6})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+35} & = & \color{red}{-18x} +15 \\\Leftrightarrow & -168x \color{red}{+35} \color{blue}{-35} \color{blue}{+18x} & = & \color{red}{-18x} +15 \color{blue}{+18x} \color{blue}{-35} \\\Leftrightarrow & -168x+18x& = & 15-35 \\\Leftrightarrow & \color{red}{-150} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-150} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{165x} +30 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{-132} \\\Leftrightarrow & 880x-165x& = & 30-132 \\\Leftrightarrow & \color{red}{715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{715} & & \\ & V = \left\{ \frac{-102}{715} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{9})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{16}{9}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{176}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-176} & = & \color{red}{495x} +90 \\\Leftrightarrow & 1188x \color{red}{-176} \color{blue}{+176} \color{blue}{-495x} & = & \color{red}{495x} +90 \color{blue}{-495x} \color{blue}{+176} \\\Leftrightarrow & 1188x-495x& = & 90+176 \\\Leftrightarrow & \color{red}{693} x& = & 266 \\\Leftrightarrow & x = \frac{266}{693} & & \\\Leftrightarrow & x = \frac{38}{99} & & \\ & V = \left\{ \frac{38}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{12}{11}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-12} & = & \color{red}{-99x} +2 \\\Leftrightarrow & -220x \color{red}{-12} \color{blue}{+12} \color{blue}{+99x} & = & \color{red}{-99x} +2 \color{blue}{+99x} \color{blue}{+12} \\\Leftrightarrow & -220x+99x& = & 2+12 \\\Leftrightarrow & \color{red}{-121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-121} & & \\\Leftrightarrow & x = \frac{-14}{121} & & \\ & V = \left\{ \frac{-14}{121} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{3})& = & 4x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{10}{3}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+110} & = & \color{red}{132x} +6 \\\Leftrightarrow & 825x \color{red}{+110} \color{blue}{-110} \color{blue}{-132x} & = & \color{red}{132x} +6 \color{blue}{-132x} \color{blue}{-110} \\\Leftrightarrow & 825x-132x& = & 6-110 \\\Leftrightarrow & \color{red}{693} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{693} & & \\ & V = \left\{ \frac{-104}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & -3x+\frac{7}{4} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+48} & = & \color{red}{-60x} +35 \\\Leftrightarrow & 160x \color{red}{+48} \color{blue}{-48} \color{blue}{+60x} & = & \color{red}{-60x} +35 \color{blue}{+60x} \color{blue}{-48} \\\Leftrightarrow & 160x+60x& = & 35-48 \\\Leftrightarrow & \color{red}{220} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{220} & & \\ & V = \left\{ \frac{-13}{220} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{20}{3}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-140} & = & \color{red}{63x} +30 \\\Leftrightarrow & 210x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & 210x-63x& = & 30+140 \\\Leftrightarrow & \color{red}{147} x& = & 170 \\\Leftrightarrow & x = \frac{170}{147} & & \\ & V = \left\{ \frac{170}{147} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{16}{7}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-32} & = & \color{red}{-126x} +35 \\\Leftrightarrow & 280x \color{red}{-32} \color{blue}{+32} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{+32} \\\Leftrightarrow & 280x+126x& = & 35+32 \\\Leftrightarrow & \color{red}{406} x& = & 67 \\\Leftrightarrow & x = \frac{67}{406} & & \\ & V = \left\{ \frac{67}{406} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -540x+225x& = & 40-108 \\\Leftrightarrow & \color{red}{-315} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-315} & & \\\Leftrightarrow & x = \frac{68}{315} & & \\ & V = \left\{ \frac{68}{315} \right\} & \\\end{align}\)