Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{6}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-6} & = & \color{red}{35x} +10 \\\Leftrightarrow & 56x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & 56x-35x& = & 10+6 \\\Leftrightarrow & \color{red}{21} x& = & 16 \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{392x} +63 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{-392x} & = & \color{red}{392x} +63 \color{blue}{-392x} \color{blue}{-48} \\\Leftrightarrow & -336x-392x& = & 63-48 \\\Leftrightarrow & \color{red}{-728} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-728} & & \\\Leftrightarrow & x = \frac{-15}{728} & & \\ & V = \left\{ \frac{-15}{728} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & -4x+\frac{7}{8} \\\Leftrightarrow & -25x+\frac{10}{3}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+80} & = & \color{red}{-96x} +21 \\\Leftrightarrow & -600x \color{red}{+80} \color{blue}{-80} \color{blue}{+96x} & = & \color{red}{-96x} +21 \color{blue}{+96x} \color{blue}{-80} \\\Leftrightarrow & -600x+96x& = & 21-80 \\\Leftrightarrow & \color{red}{-504} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-504} & & \\\Leftrightarrow & x = \frac{59}{504} & & \\ & V = \left\{ \frac{59}{504} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{4})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x-\frac{21}{4}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-280}{ \color{blue}{20} }x- \frac{105}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{-60x} +24 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{+60x} & = & \color{red}{-60x} +24 \color{blue}{+60x} \color{blue}{+105} \\\Leftrightarrow & -280x+60x& = & 24+105 \\\Leftrightarrow & \color{red}{-220} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-220} & & \\\Leftrightarrow & x = \frac{-129}{220} & & \\ & V = \left\{ \frac{-129}{220} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{11})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x-\frac{10}{11}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-50} & = & \color{red}{385x} +77 \\\Leftrightarrow & -330x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +77 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & -330x-385x& = & 77+50 \\\Leftrightarrow & \color{red}{-715} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-715} & & \\\Leftrightarrow & x = \frac{-127}{715} & & \\ & V = \left\{ \frac{-127}{715} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+72} & = & \color{red}{105x} +10 \\\Leftrightarrow & -360x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & -360x-105x& = & 10-72 \\\Leftrightarrow & \color{red}{-465} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-465} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -14x-\frac{14}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-14} & = & \color{red}{9x} +8 \\\Leftrightarrow & -42x \color{red}{-14} \color{blue}{+14} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{+14} \\\Leftrightarrow & -42x-9x& = & 8+14 \\\Leftrightarrow & \color{red}{-51} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-51} & & \\\Leftrightarrow & x = \frac{-22}{51} & & \\ & V = \left\{ \frac{-22}{51} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -20x-\frac{8}{3}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{135x} +27 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +27 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -300x-135x& = & 27+40 \\\Leftrightarrow & \color{red}{-435} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-435} & & \\\Leftrightarrow & x = \frac{-67}{435} & & \\ & V = \left\{ \frac{-67}{435} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{3})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{4}{3}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+12} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -54x \color{red}{+12} \color{blue}{-12} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-12} \\\Leftrightarrow & -54x+63x& = & 10-12 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{4})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -35x+\frac{21}{4}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-700}{ \color{blue}{20} }x+ \frac{105}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -700x \color{red}{+105} & = & \color{red}{180x} +32 \\\Leftrightarrow & -700x \color{red}{+105} \color{blue}{-105} \color{blue}{-180x} & = & \color{red}{180x} +32 \color{blue}{-180x} \color{blue}{-105} \\\Leftrightarrow & -700x-180x& = & 32-105 \\\Leftrightarrow & \color{red}{-880} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-880} & & \\\Leftrightarrow & x = \frac{73}{880} & & \\ & V = \left\{ \frac{73}{880} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{9})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{25}{9}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{175}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+175} & = & \color{red}{567x} +90 \\\Leftrightarrow & 1260x \color{red}{+175} \color{blue}{-175} \color{blue}{-567x} & = & \color{red}{567x} +90 \color{blue}{-567x} \color{blue}{-175} \\\Leftrightarrow & 1260x-567x& = & 90-175 \\\Leftrightarrow & \color{red}{693} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{693} & & \\ & V = \left\{ \frac{-85}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+63} & = & \color{red}{175x} +50 \\\Leftrightarrow & 420x \color{red}{+63} \color{blue}{-63} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-63} \\\Leftrightarrow & 420x-175x& = & 50-63 \\\Leftrightarrow & \color{red}{245} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{245} & & \\ & V = \left\{ \frac{-13}{245} \right\} & \\\end{align}\)