Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{75x} +40 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+12} \\\Leftrightarrow & 90x-75x& = & 40+12 \\\Leftrightarrow & \color{red}{15} x& = & 52 \\\Leftrightarrow & x = \frac{52}{15} & & \\ & V = \left\{ \frac{52}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{9})& = & -6x+\frac{6}{7} \\\Leftrightarrow & 25x+\frac{25}{9}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{-378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{+175} & = & \color{red}{-378x} +54 \\\Leftrightarrow & 1575x \color{red}{+175} \color{blue}{-175} \color{blue}{+378x} & = & \color{red}{-378x} +54 \color{blue}{+378x} \color{blue}{-175} \\\Leftrightarrow & 1575x+378x& = & 54-175 \\\Leftrightarrow & \color{red}{1953} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{1953} & & \\ & V = \left\{ \frac{-121}{1953} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{9})& = & -4x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{10}{9}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{+110} & = & \color{red}{-396x} +18 \\\Leftrightarrow & 2475x \color{red}{+110} \color{blue}{-110} \color{blue}{+396x} & = & \color{red}{-396x} +18 \color{blue}{+396x} \color{blue}{-110} \\\Leftrightarrow & 2475x+396x& = & 18-110 \\\Leftrightarrow & \color{red}{2871} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{2871} & & \\ & V = \left\{ \frac{-92}{2871} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -35x-\frac{35}{3}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{54x} +15 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{+70} \\\Leftrightarrow & -210x-54x& = & 15+70 \\\Leftrightarrow & \color{red}{-264} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-264} & & \\\Leftrightarrow & x = \frac{-85}{264} & & \\ & V = \left\{ \frac{-85}{264} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-150} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 660x \color{red}{-150} \color{blue}{+150} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+150} \\\Leftrightarrow & 660x+385x& = & 66+150 \\\Leftrightarrow & \color{red}{1045} x& = & 216 \\\Leftrightarrow & x = \frac{216}{1045} & & \\ & V = \left\{ \frac{216}{1045} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 8+12 \\\Leftrightarrow & \color{red}{-115} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-115} & & \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x+\frac{9}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+9} & = & \color{red}{55x} +6 \\\Leftrightarrow & -99x \color{red}{+9} \color{blue}{-9} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-9} \\\Leftrightarrow & -99x-55x& = & 6-9 \\\Leftrightarrow & \color{red}{-154} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-154} & & \\\Leftrightarrow & x = \frac{3}{154} & & \\ & V = \left\{ \frac{3}{154} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{11})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 14x+\frac{14}{11}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x+ \frac{126}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{+126} & = & \color{red}{297x} +22 \\\Leftrightarrow & 1386x \color{red}{+126} \color{blue}{-126} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{-126} \\\Leftrightarrow & 1386x-297x& = & 22-126 \\\Leftrightarrow & \color{red}{1089} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{1089} & & \\ & V = \left\{ \frac{-104}{1089} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+18} & = & \color{red}{168x} +56 \\\Leftrightarrow & -315x \color{red}{+18} \color{blue}{-18} \color{blue}{-168x} & = & \color{red}{168x} +56 \color{blue}{-168x} \color{blue}{-18} \\\Leftrightarrow & -315x-168x& = & 56-18 \\\Leftrightarrow & \color{red}{-483} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-483} & & \\\Leftrightarrow & x = \frac{-38}{483} & & \\ & V = \left\{ \frac{-38}{483} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+12} & = & \color{red}{-45x} +6 \\\Leftrightarrow & 100x \color{red}{+12} \color{blue}{-12} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-12} \\\Leftrightarrow & 100x+45x& = & 6-12 \\\Leftrightarrow & \color{red}{145} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{145} & & \\ & V = \left\{ \frac{-6}{145} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{3})& = & -9x+\frac{5}{9} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-24} & = & \color{red}{-81x} +5 \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+81x} & = & \color{red}{-81x} +5 \color{blue}{+81x} \color{blue}{+24} \\\Leftrightarrow & -36x+81x& = & 5+24 \\\Leftrightarrow & \color{red}{45} x& = & 29 \\\Leftrightarrow & x = \frac{29}{45} & & \\ & V = \left\{ \frac{29}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{9})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 10x-\frac{10}{9}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{900}{ \color{blue}{90} }x- \frac{100}{ \color{blue}{90} })& = & (\frac{630}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 900x \color{red}{-100} & = & \color{red}{630x} +63 \\\Leftrightarrow & 900x \color{red}{-100} \color{blue}{+100} \color{blue}{-630x} & = & \color{red}{630x} +63 \color{blue}{-630x} \color{blue}{+100} \\\Leftrightarrow & 900x-630x& = & 63+100 \\\Leftrightarrow & \color{red}{270} x& = & 163 \\\Leftrightarrow & x = \frac{163}{270} & & \\ & V = \left\{ \frac{163}{270} \right\} & \\\end{align}\)