Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{10}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-10} & = & \color{red}{81x} +6 \\\Leftrightarrow & 90x \color{red}{-10} \color{blue}{+10} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{+10} \\\Leftrightarrow & 90x-81x& = & 6+10 \\\Leftrightarrow & \color{red}{9} x& = & 16 \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{-315x} +15 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{+315x} & = & \color{red}{-315x} +15 \color{blue}{+315x} \color{blue}{+84} \\\Leftrightarrow & -280x+315x& = & 15+84 \\\Leftrightarrow & \color{red}{35} x& = & 99 \\\Leftrightarrow & x = \frac{99}{35} & & \\ & V = \left\{ \frac{99}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-30} & = & \color{red}{42x} +14 \\\Leftrightarrow & 315x \color{red}{-30} \color{blue}{+30} \color{blue}{-42x} & = & \color{red}{42x} +14 \color{blue}{-42x} \color{blue}{+30} \\\Leftrightarrow & 315x-42x& = & 14+30 \\\Leftrightarrow & \color{red}{273} x& = & 44 \\\Leftrightarrow & x = \frac{44}{273} & & \\ & V = \left\{ \frac{44}{273} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{18}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{54}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & 252x+105x& = & 35-54 \\\Leftrightarrow & \color{red}{357} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{357} & & \\ & V = \left\{ \frac{-19}{357} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{2})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{15}{2}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{-45} & = & \color{red}{42x} +4 \\\Leftrightarrow & -36x \color{red}{-45} \color{blue}{+45} \color{blue}{-42x} & = & \color{red}{42x} +4 \color{blue}{-42x} \color{blue}{+45} \\\Leftrightarrow & -36x-42x& = & 4+45 \\\Leftrightarrow & \color{red}{-78} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-78} & & \\\Leftrightarrow & x = \frac{-49}{78} & & \\ & V = \left\{ \frac{-49}{78} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{-48} & = & \color{red}{100x} +35 \\\Leftrightarrow & 120x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & 120x-100x& = & 35+48 \\\Leftrightarrow & \color{red}{20} x& = & 83 \\\Leftrightarrow & x = \frac{83}{20} & & \\ & V = \left\{ \frac{83}{20} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{6})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 28x-\frac{35}{6}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{10}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-35} & = & \color{red}{54x} +10 \\\Leftrightarrow & 168x \color{red}{-35} \color{blue}{+35} \color{blue}{-54x} & = & \color{red}{54x} +10 \color{blue}{-54x} \color{blue}{+35} \\\Leftrightarrow & 168x-54x& = & 10+35 \\\Leftrightarrow & \color{red}{114} x& = & 45 \\\Leftrightarrow & x = \frac{45}{114} & & \\\Leftrightarrow & x = \frac{15}{38} & & \\ & V = \left\{ \frac{15}{38} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{+40} & = & \color{red}{315x} +54 \\\Leftrightarrow & 450x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & 450x-315x& = & 54-40 \\\Leftrightarrow & \color{red}{135} x& = & 14 \\\Leftrightarrow & x = \frac{14}{135} & & \\ & V = \left\{ \frac{14}{135} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{-245x} +45 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 1050x+245x& = & 45-84 \\\Leftrightarrow & \color{red}{1295} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{1295} & & \\ & V = \left\{ \frac{-39}{1295} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{8})& = & -8x+\frac{3}{4} \\\Leftrightarrow & -25x-\frac{15}{8}& = & -8x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-15} & = & \color{red}{-64x} +6 \\\Leftrightarrow & -200x \color{red}{-15} \color{blue}{+15} \color{blue}{+64x} & = & \color{red}{-64x} +6 \color{blue}{+64x} \color{blue}{+15} \\\Leftrightarrow & -200x+64x& = & 6+15 \\\Leftrightarrow & \color{red}{-136} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-136} & & \\\Leftrightarrow & x = \frac{-21}{136} & & \\ & V = \left\{ \frac{-21}{136} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{-85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-85} & & \\\Leftrightarrow & x = \frac{6}{85} & & \\ & V = \left\{ \frac{6}{85} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{3})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -8x+\frac{10}{3}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+110} & = & \color{red}{-297x} +27 \\\Leftrightarrow & -264x \color{red}{+110} \color{blue}{-110} \color{blue}{+297x} & = & \color{red}{-297x} +27 \color{blue}{+297x} \color{blue}{-110} \\\Leftrightarrow & -264x+297x& = & 27-110 \\\Leftrightarrow & \color{red}{33} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{33} & & \\ & V = \left\{ \frac{-83}{33} \right\} & \\\end{align}\)