Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{588x} +35 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{-120} \\\Leftrightarrow & 840x-588x& = & 35-120 \\\Leftrightarrow & \color{red}{252} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{252} & & \\ & V = \left\{ \frac{-85}{252} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{2})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -28x+\frac{21}{2}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+63} & = & \color{red}{-30x} +4 \\\Leftrightarrow & -168x \color{red}{+63} \color{blue}{-63} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{-63} \\\Leftrightarrow & -168x+30x& = & 4-63 \\\Leftrightarrow & \color{red}{-138} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-138} & & \\\Leftrightarrow & x = \frac{59}{138} & & \\ & V = \left\{ \frac{59}{138} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+32} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -216x \color{red}{+32} \color{blue}{-32} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-32} \\\Leftrightarrow & -216x+252x& = & 21-32 \\\Leftrightarrow & \color{red}{36} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{36} & & \\ & V = \left\{ \frac{-11}{36} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 16x+\frac{8}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{320}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 320x \color{red}{+32} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 320x \color{red}{+32} \color{blue}{-32} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-32} \\\Leftrightarrow & 320x+100x& = & 45-32 \\\Leftrightarrow & \color{red}{420} x& = & 13 \\\Leftrightarrow & x = \frac{13}{420} & & \\ & V = \left\{ \frac{13}{420} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-210} & = & \color{red}{385x} +22 \\\Leftrightarrow & 1848x \color{red}{-210} \color{blue}{+210} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+210} \\\Leftrightarrow & 1848x-385x& = & 22+210 \\\Leftrightarrow & \color{red}{1463} x& = & 232 \\\Leftrightarrow & x = \frac{232}{1463} & & \\ & V = \left\{ \frac{232}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-12} & = & \color{red}{126x} +35 \\\Leftrightarrow & -112x \color{red}{-12} \color{blue}{+12} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{+12} \\\Leftrightarrow & -112x-126x& = & 35+12 \\\Leftrightarrow & \color{red}{-238} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-238} & & \\\Leftrightarrow & x = \frac{-47}{238} & & \\ & V = \left\{ \frac{-47}{238} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{9})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{20}{9}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-40} & = & \color{red}{54x} +15 \\\Leftrightarrow & -144x \color{red}{-40} \color{blue}{+40} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{+40} \\\Leftrightarrow & -144x-54x& = & 15+40 \\\Leftrightarrow & \color{red}{-198} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-198} & & \\\Leftrightarrow & x = \frac{-5}{18} & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 540x+225x& = & 10+108 \\\Leftrightarrow & \color{red}{765} x& = & 118 \\\Leftrightarrow & x = \frac{118}{765} & & \\ & V = \left\{ \frac{118}{765} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+24} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 264x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & 264x+55x& = & 5-24 \\\Leftrightarrow & \color{red}{319} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{319} & & \\ & V = \left\{ \frac{-19}{319} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{11})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -20x+\frac{10}{11}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{+40} & = & \color{red}{-396x} +55 \\\Leftrightarrow & -880x \color{red}{+40} \color{blue}{-40} \color{blue}{+396x} & = & \color{red}{-396x} +55 \color{blue}{+396x} \color{blue}{-40} \\\Leftrightarrow & -880x+396x& = & 55-40 \\\Leftrightarrow & \color{red}{-484} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-484} & & \\\Leftrightarrow & x = \frac{-15}{484} & & \\ & V = \left\{ \frac{-15}{484} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{4})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{-84x} +5 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +5 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & -120x+84x& = & 5-45 \\\Leftrightarrow & \color{red}{-36} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-36} & & \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{+16} & = & \color{red}{-18x} +9 \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{+18x} & = & \color{red}{-18x} +9 \color{blue}{+18x} \color{blue}{-16} \\\Leftrightarrow & 24x+18x& = & 9-16 \\\Leftrightarrow & \color{red}{42} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{42} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)