Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -30x+\frac{24}{11}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+168} & = & \color{red}{-539x} +33 \\\Leftrightarrow & -2310x \color{red}{+168} \color{blue}{-168} \color{blue}{+539x} & = & \color{red}{-539x} +33 \color{blue}{+539x} \color{blue}{-168} \\\Leftrightarrow & -2310x+539x& = & 33-168 \\\Leftrightarrow & \color{red}{-1771} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{-1771} & & \\\Leftrightarrow & x = \frac{135}{1771} & & \\ & V = \left\{ \frac{135}{1771} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1188}{ \color{blue}{66} }x+ \frac{180}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1188x \color{red}{+180} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 1188x \color{red}{+180} \color{blue}{-180} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-180} \\\Leftrightarrow & 1188x+330x& = & 55-180 \\\Leftrightarrow & \color{red}{1518} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1518} & & \\ & V = \left\{ \frac{-125}{1518} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{-60} & = & \color{red}{490x} +63 \\\Leftrightarrow & -700x \color{red}{-60} \color{blue}{+60} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+60} \\\Leftrightarrow & -700x-490x& = & 63+60 \\\Leftrightarrow & \color{red}{-1190} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-1190} & & \\\Leftrightarrow & x = \frac{-123}{1190} & & \\ & V = \left\{ \frac{-123}{1190} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-630}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -630x \color{red}{+120} & = & \color{red}{168x} +35 \\\Leftrightarrow & -630x \color{red}{+120} \color{blue}{-120} \color{blue}{-168x} & = & \color{red}{168x} +35 \color{blue}{-168x} \color{blue}{-120} \\\Leftrightarrow & -630x-168x& = & 35-120 \\\Leftrightarrow & \color{red}{-798} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-798} & & \\\Leftrightarrow & x = \frac{85}{798} & & \\ & V = \left\{ \frac{85}{798} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{9})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-220} & = & \color{red}{297x} +54 \\\Leftrightarrow & 1980x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +54 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 1980x-297x& = & 54+220 \\\Leftrightarrow & \color{red}{1683} x& = & 274 \\\Leftrightarrow & x = \frac{274}{1683} & & \\ & V = \left\{ \frac{274}{1683} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{-20} & = & \color{red}{70x} +21 \\\Leftrightarrow & -56x \color{red}{-20} \color{blue}{+20} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{+20} \\\Leftrightarrow & -56x-70x& = & 21+20 \\\Leftrightarrow & \color{red}{-126} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-126} & & \\\Leftrightarrow & x = \frac{-41}{126} & & \\ & V = \left\{ \frac{-41}{126} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{9})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{20}{9}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-40} & = & \color{red}{-162x} +81 \\\Leftrightarrow & -144x \color{red}{-40} \color{blue}{+40} \color{blue}{+162x} & = & \color{red}{-162x} +81 \color{blue}{+162x} \color{blue}{+40} \\\Leftrightarrow & -144x+162x& = & 81+40 \\\Leftrightarrow & \color{red}{18} x& = & 121 \\\Leftrightarrow & x = \frac{121}{18} & & \\ & V = \left\{ \frac{121}{18} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -25x-\frac{25}{12}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{-25} & = & \color{red}{-84x} +16 \\\Leftrightarrow & -300x \color{red}{-25} \color{blue}{+25} \color{blue}{+84x} & = & \color{red}{-84x} +16 \color{blue}{+84x} \color{blue}{+25} \\\Leftrightarrow & -300x+84x& = & 16+25 \\\Leftrightarrow & \color{red}{-216} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-216} & & \\\Leftrightarrow & x = \frac{-41}{216} & & \\ & V = \left\{ \frac{-41}{216} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-220} & = & \color{red}{297x} +18 \\\Leftrightarrow & -264x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & -264x-297x& = & 18+220 \\\Leftrightarrow & \color{red}{-561} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-561} & & \\\Leftrightarrow & x = \frac{-14}{33} & & \\ & V = \left\{ \frac{-14}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{5})& = & -4x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{9}{5}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-99} & = & \color{red}{-220x} +40 \\\Leftrightarrow & 825x \color{red}{-99} \color{blue}{+99} \color{blue}{+220x} & = & \color{red}{-220x} +40 \color{blue}{+220x} \color{blue}{+99} \\\Leftrightarrow & 825x+220x& = & 40+99 \\\Leftrightarrow & \color{red}{1045} x& = & 139 \\\Leftrightarrow & x = \frac{139}{1045} & & \\ & V = \left\{ \frac{139}{1045} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{8}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-8} & = & \color{red}{55x} +6 \\\Leftrightarrow & -132x \color{red}{-8} \color{blue}{+8} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+8} \\\Leftrightarrow & -132x-55x& = & 6+8 \\\Leftrightarrow & \color{red}{-187} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-187} & & \\\Leftrightarrow & x = \frac{-14}{187} & & \\ & V = \left\{ \frac{-14}{187} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-126x} +63 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{+20} \\\Leftrightarrow & 140x+126x& = & 63+20 \\\Leftrightarrow & \color{red}{266} x& = & 83 \\\Leftrightarrow & x = \frac{83}{266} & & \\ & V = \left\{ \frac{83}{266} \right\} & \\\end{align}\)