Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{15}{4}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{60x} +10 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +10 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & 72x-60x& = & 10+45 \\\Leftrightarrow & \color{red}{12} x& = & 55 \\\Leftrightarrow & x = \frac{55}{12} & & \\ & V = \left\{ \frac{55}{12} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & -8x+\frac{7}{5} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -8x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{-40x} +7 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{+24} \\\Leftrightarrow & -90x+40x& = & 7+24 \\\Leftrightarrow & \color{red}{-50} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-50} & & \\\Leftrightarrow & x = \frac{-31}{50} & & \\ & V = \left\{ \frac{-31}{50} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{15}{11}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-75} & = & \color{red}{110x} +66 \\\Leftrightarrow & 495x \color{red}{-75} \color{blue}{+75} \color{blue}{-110x} & = & \color{red}{110x} +66 \color{blue}{-110x} \color{blue}{+75} \\\Leftrightarrow & 495x-110x& = & 66+75 \\\Leftrightarrow & \color{red}{385} x& = & 141 \\\Leftrightarrow & x = \frac{141}{385} & & \\ & V = \left\{ \frac{141}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+108} & = & \color{red}{315x} +20 \\\Leftrightarrow & 270x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 270x-315x& = & 20-108 \\\Leftrightarrow & \color{red}{-45} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-45} & & \\\Leftrightarrow & x = \frac{88}{45} & & \\ & V = \left\{ \frac{88}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{2})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{9}{2}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-36}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -36x \color{red}{+27} & = & \color{red}{-42x} +8 \\\Leftrightarrow & -36x \color{red}{+27} \color{blue}{-27} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{-27} \\\Leftrightarrow & -36x+42x& = & 8-27 \\\Leftrightarrow & \color{red}{6} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{6} & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{11})& = & -8x+\frac{9}{5} \\\Leftrightarrow & -18x+\frac{24}{11}& = & -8x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+120} & = & \color{red}{-440x} +99 \\\Leftrightarrow & -990x \color{red}{+120} \color{blue}{-120} \color{blue}{+440x} & = & \color{red}{-440x} +99 \color{blue}{+440x} \color{blue}{-120} \\\Leftrightarrow & -990x+440x& = & 99-120 \\\Leftrightarrow & \color{red}{-550} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-550} & & \\\Leftrightarrow & x = \frac{21}{550} & & \\ & V = \left\{ \frac{21}{550} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 25x-\frac{15}{7}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-135} & = & \color{red}{-504x} +14 \\\Leftrightarrow & 1575x \color{red}{-135} \color{blue}{+135} \color{blue}{+504x} & = & \color{red}{-504x} +14 \color{blue}{+504x} \color{blue}{+135} \\\Leftrightarrow & 1575x+504x& = & 14+135 \\\Leftrightarrow & \color{red}{2079} x& = & 149 \\\Leftrightarrow & x = \frac{149}{2079} & & \\ & V = \left\{ \frac{149}{2079} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{5})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 10x+\frac{6}{5}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+42} & = & \color{red}{315x} +45 \\\Leftrightarrow & 350x \color{red}{+42} \color{blue}{-42} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{-42} \\\Leftrightarrow & 350x-315x& = & 45-42 \\\Leftrightarrow & \color{red}{35} x& = & 3 \\\Leftrightarrow & x = \frac{3}{35} & & \\ & V = \left\{ \frac{3}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{30x} +15 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +15 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & -24x-30x& = & 15-16 \\\Leftrightarrow & \color{red}{-54} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-54} & & \\\Leftrightarrow & x = \frac{1}{54} & & \\ & V = \left\{ \frac{1}{54} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+56} & = & \color{red}{-63x} +15 \\\Leftrightarrow & 420x \color{red}{+56} \color{blue}{-56} \color{blue}{+63x} & = & \color{red}{-63x} +15 \color{blue}{+63x} \color{blue}{-56} \\\Leftrightarrow & 420x+63x& = & 15-56 \\\Leftrightarrow & \color{red}{483} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{483} & & \\ & V = \left\{ \frac{-41}{483} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{105x} +56 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-30} \\\Leftrightarrow & 126x-105x& = & 56-30 \\\Leftrightarrow & \color{red}{21} x& = & 26 \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 4x+\frac{4}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{189x} +56 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-12} \\\Leftrightarrow & 84x-189x& = & 56-12 \\\Leftrightarrow & \color{red}{-105} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-105} & & \\\Leftrightarrow & x = \frac{-44}{105} & & \\ & V = \left\{ \frac{-44}{105} \right\} & \\\end{align}\)