Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -16x+\frac{8}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+88} & = & \color{red}{385x} +25 \\\Leftrightarrow & -880x \color{red}{+88} \color{blue}{-88} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{-88} \\\Leftrightarrow & -880x-385x& = & 25-88 \\\Leftrightarrow & \color{red}{-1265} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-1265} & & \\\Leftrightarrow & x = \frac{63}{1265} & & \\ & V = \left\{ \frac{63}{1265} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{35x} +2 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -120x-35x& = & 2-12 \\\Leftrightarrow & \color{red}{-155} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-155} & & \\\Leftrightarrow & x = \frac{2}{31} & & \\ & V = \left\{ \frac{2}{31} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & 300x+70x& = & 45+24 \\\Leftrightarrow & \color{red}{370} x& = & 69 \\\Leftrightarrow & x = \frac{69}{370} & & \\ & V = \left\{ \frac{69}{370} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+36} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 450x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 450x+105x& = & 10-36 \\\Leftrightarrow & \color{red}{555} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{555} & & \\ & V = \left\{ \frac{-26}{555} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 90x+63x& = & 6+8 \\\Leftrightarrow & \color{red}{153} x& = & 14 \\\Leftrightarrow & x = \frac{14}{153} & & \\ & V = \left\{ \frac{14}{153} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{2})& = & -4x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{21}{2}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{42}{ \color{blue}{2} }x- \frac{21}{ \color{blue}{2} })& = & (\frac{-8}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 42x \color{red}{-21} & = & \color{red}{-8x} +9 \\\Leftrightarrow & 42x \color{red}{-21} \color{blue}{+21} \color{blue}{+8x} & = & \color{red}{-8x} +9 \color{blue}{+8x} \color{blue}{+21} \\\Leftrightarrow & 42x+8x& = & 9+21 \\\Leftrightarrow & \color{red}{50} x& = & 30 \\\Leftrightarrow & x = \frac{30}{50} & & \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & 4x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{10}{11}& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1650}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{440}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1650x \color{red}{+100} & = & \color{red}{440x} +99 \\\Leftrightarrow & 1650x \color{red}{+100} \color{blue}{-100} \color{blue}{-440x} & = & \color{red}{440x} +99 \color{blue}{-440x} \color{blue}{-100} \\\Leftrightarrow & 1650x-440x& = & 99-100 \\\Leftrightarrow & \color{red}{1210} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1210} & & \\ & V = \left\{ \frac{-1}{1210} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & 3x+\frac{3}{5} \\\Leftrightarrow & -20x-\frac{12}{7}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-60} & = & \color{red}{105x} +21 \\\Leftrightarrow & -700x \color{red}{-60} \color{blue}{+60} \color{blue}{-105x} & = & \color{red}{105x} +21 \color{blue}{-105x} \color{blue}{+60} \\\Leftrightarrow & -700x-105x& = & 21+60 \\\Leftrightarrow & \color{red}{-805} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-805} & & \\\Leftrightarrow & x = \frac{-81}{805} & & \\ & V = \left\{ \frac{-81}{805} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -4x-\frac{4}{5}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{-28} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -140x \color{red}{-28} \color{blue}{+28} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+28} \\\Leftrightarrow & -140x+315x& = & 20+28 \\\Leftrightarrow & \color{red}{175} x& = & 48 \\\Leftrightarrow & x = \frac{48}{175} & & \\ & V = \left\{ \frac{48}{175} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-80} & = & \color{red}{-210x} +27 \\\Leftrightarrow & 300x \color{red}{-80} \color{blue}{+80} \color{blue}{+210x} & = & \color{red}{-210x} +27 \color{blue}{+210x} \color{blue}{+80} \\\Leftrightarrow & 300x+210x& = & 27+80 \\\Leftrightarrow & \color{red}{510} x& = & 107 \\\Leftrightarrow & x = \frac{107}{510} & & \\ & V = \left\{ \frac{107}{510} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+16} & = & \color{red}{162x} +15 \\\Leftrightarrow & 360x \color{red}{+16} \color{blue}{-16} \color{blue}{-162x} & = & \color{red}{162x} +15 \color{blue}{-162x} \color{blue}{-16} \\\Leftrightarrow & 360x-162x& = & 15-16 \\\Leftrightarrow & \color{red}{198} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{198} & & \\ & V = \left\{ \frac{-1}{198} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{245x} +45 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{-28} \\\Leftrightarrow & -210x-245x& = & 45-28 \\\Leftrightarrow & \color{red}{-455} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-455} & & \\\Leftrightarrow & x = \frac{-17}{455} & & \\ & V = \left\{ \frac{-17}{455} \right\} & \\\end{align}\)