Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{16}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{176}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-176} & = & \color{red}{-385x} +20 \\\Leftrightarrow & -880x \color{red}{-176} \color{blue}{+176} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{+176} \\\Leftrightarrow & -880x+385x& = & 20+176 \\\Leftrightarrow & \color{red}{-495} x& = & 196 \\\Leftrightarrow & x = \frac{196}{-495} & & \\\Leftrightarrow & x = \frac{-196}{495} & & \\ & V = \left\{ \frac{-196}{495} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-28} \\\Leftrightarrow & -210x+245x& = & 50-28 \\\Leftrightarrow & \color{red}{35} x& = & 22 \\\Leftrightarrow & x = \frac{22}{35} & & \\ & V = \left\{ \frac{22}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -24x+\frac{24}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{35x} +4 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-24} \\\Leftrightarrow & -168x-35x& = & 4-24 \\\Leftrightarrow & \color{red}{-203} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-203} & & \\\Leftrightarrow & x = \frac{20}{203} & & \\ & V = \left\{ \frac{20}{203} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{9})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{16}{9}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x+ \frac{32}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{+32} & = & \color{red}{-162x} +27 \\\Leftrightarrow & -144x \color{red}{+32} \color{blue}{-32} \color{blue}{+162x} & = & \color{red}{-162x} +27 \color{blue}{+162x} \color{blue}{-32} \\\Leftrightarrow & -144x+162x& = & 27-32 \\\Leftrightarrow & \color{red}{18} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{18} & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{-40} & = & \color{red}{18x} +15 \\\Leftrightarrow & 48x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +15 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & 48x-18x& = & 15+40 \\\Leftrightarrow & \color{red}{30} x& = & 55 \\\Leftrightarrow & x = \frac{55}{30} & & \\\Leftrightarrow & x = \frac{11}{6} & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 8x-\frac{8}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{-490x} +49 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{+80} \\\Leftrightarrow & 560x+490x& = & 49+80 \\\Leftrightarrow & \color{red}{1050} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1050} & & \\\Leftrightarrow & x = \frac{43}{350} & & \\ & V = \left\{ \frac{43}{350} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -20x+\frac{10}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+20} & = & \color{red}{-54x} +9 \\\Leftrightarrow & -120x \color{red}{+20} \color{blue}{-20} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-20} \\\Leftrightarrow & -120x+54x& = & 9-20 \\\Leftrightarrow & \color{red}{-66} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-66} & & \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & 75x+35x& = & 7-12 \\\Leftrightarrow & \color{red}{110} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{110} & & \\\Leftrightarrow & x = \frac{-1}{22} & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{5})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+126} & = & \color{red}{-360x} +10 \\\Leftrightarrow & 945x \color{red}{+126} \color{blue}{-126} \color{blue}{+360x} & = & \color{red}{-360x} +10 \color{blue}{+360x} \color{blue}{-126} \\\Leftrightarrow & 945x+360x& = & 10-126 \\\Leftrightarrow & \color{red}{1305} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{1305} & & \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & 1050x+245x& = & 42+150 \\\Leftrightarrow & \color{red}{1295} x& = & 192 \\\Leftrightarrow & x = \frac{192}{1295} & & \\ & V = \left\{ \frac{192}{1295} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{-85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-85} & & \\\Leftrightarrow & x = \frac{6}{85} & & \\ & V = \left\{ \frac{6}{85} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{12})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -20x-\frac{25}{12}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{75}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-75} & = & \color{red}{324x} +16 \\\Leftrightarrow & -720x \color{red}{-75} \color{blue}{+75} \color{blue}{-324x} & = & \color{red}{324x} +16 \color{blue}{-324x} \color{blue}{+75} \\\Leftrightarrow & -720x-324x& = & 16+75 \\\Leftrightarrow & \color{red}{-1044} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-1044} & & \\\Leftrightarrow & x = \frac{-91}{1044} & & \\ & V = \left\{ \frac{-91}{1044} \right\} & \\\end{align}\)