Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -10x+\frac{4}{3}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+20} & = & \color{red}{-105x} +12 \\\Leftrightarrow & -150x \color{red}{+20} \color{blue}{-20} \color{blue}{+105x} & = & \color{red}{-105x} +12 \color{blue}{+105x} \color{blue}{-20} \\\Leftrightarrow & -150x+105x& = & 12-20 \\\Leftrightarrow & \color{red}{-45} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-45} & & \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{105x} +27 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & 84x-105x& = & 27-56 \\\Leftrightarrow & \color{red}{-21} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-21} & & \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-14} & = & \color{red}{-15x} +4 \\\Leftrightarrow & 84x \color{red}{-14} \color{blue}{+14} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+14} \\\Leftrightarrow & 84x+15x& = & 4+14 \\\Leftrightarrow & \color{red}{99} x& = & 18 \\\Leftrightarrow & x = \frac{18}{99} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+30} \\\Leftrightarrow & 140x+175x& = & 42+30 \\\Leftrightarrow & \color{red}{315} x& = & 72 \\\Leftrightarrow & x = \frac{72}{315} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -2x+\frac{3}{5} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -2x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-10x} +3 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+10x} & = & \color{red}{-10x} +3 \color{blue}{+10x} \color{blue}{+12} \\\Leftrightarrow & -90x+10x& = & 3+12 \\\Leftrightarrow & \color{red}{-80} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-80} & & \\\Leftrightarrow & x = \frac{-3}{16} & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{5})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{14}{5}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+42} & = & \color{red}{-120x} +10 \\\Leftrightarrow & -315x \color{red}{+42} \color{blue}{-42} \color{blue}{+120x} & = & \color{red}{-120x} +10 \color{blue}{+120x} \color{blue}{-42} \\\Leftrightarrow & -315x+120x& = & 10-42 \\\Leftrightarrow & \color{red}{-195} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-195} & & \\\Leftrightarrow & x = \frac{32}{195} & & \\ & V = \left\{ \frac{32}{195} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x- \frac{112}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{-112} & = & \color{red}{-108x} +27 \\\Leftrightarrow & -504x \color{red}{-112} \color{blue}{+112} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+112} \\\Leftrightarrow & -504x+108x& = & 27+112 \\\Leftrightarrow & \color{red}{-396} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-396} & & \\\Leftrightarrow & x = \frac{-139}{396} & & \\ & V = \left\{ \frac{-139}{396} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 8x-\frac{10}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-50} & = & \color{red}{-245x} +21 \\\Leftrightarrow & 280x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & 280x+245x& = & 21+50 \\\Leftrightarrow & \color{red}{525} x& = & 71 \\\Leftrightarrow & x = \frac{71}{525} & & \\ & V = \left\{ \frac{71}{525} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{11})& = & 8x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{35}{11}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-105} & = & \color{red}{264x} +110 \\\Leftrightarrow & 693x \color{red}{-105} \color{blue}{+105} \color{blue}{-264x} & = & \color{red}{264x} +110 \color{blue}{-264x} \color{blue}{+105} \\\Leftrightarrow & 693x-264x& = & 110+105 \\\Leftrightarrow & \color{red}{429} x& = & 215 \\\Leftrightarrow & x = \frac{215}{429} & & \\ & V = \left\{ \frac{215}{429} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{5})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -12x+\frac{8}{5}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{-25x} +7 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{+25x} & = & \color{red}{-25x} +7 \color{blue}{+25x} \color{blue}{-8} \\\Leftrightarrow & -60x+25x& = & 7-8 \\\Leftrightarrow & \color{red}{-35} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-35} & & \\\Leftrightarrow & x = \frac{1}{35} & & \\ & V = \left\{ \frac{1}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 9x-\frac{6}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{405}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 405x \color{red}{-54} & = & \color{red}{225x} +40 \\\Leftrightarrow & 405x \color{red}{-54} \color{blue}{+54} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+54} \\\Leftrightarrow & 405x-225x& = & 40+54 \\\Leftrightarrow & \color{red}{180} x& = & 94 \\\Leftrightarrow & x = \frac{94}{180} & & \\\Leftrightarrow & x = \frac{47}{90} & & \\ & V = \left\{ \frac{47}{90} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{5})& = & 6x+\frac{2}{11} \\\Leftrightarrow & -35x-\frac{14}{5}& = & 6x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-154} & = & \color{red}{330x} +10 \\\Leftrightarrow & -1925x \color{red}{-154} \color{blue}{+154} \color{blue}{-330x} & = & \color{red}{330x} +10 \color{blue}{-330x} \color{blue}{+154} \\\Leftrightarrow & -1925x-330x& = & 10+154 \\\Leftrightarrow & \color{red}{-2255} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-2255} & & \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)