Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +3 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +3 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 3-12 \\\Leftrightarrow & \color{red}{-85} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-85} & & \\\Leftrightarrow & x = \frac{9}{85} & & \\ & V = \left\{ \frac{9}{85} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & 6x+\frac{6}{7} \\\Leftrightarrow & -25x-\frac{10}{3}& = & 6x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-70} & = & \color{red}{126x} +18 \\\Leftrightarrow & -525x \color{red}{-70} \color{blue}{+70} \color{blue}{-126x} & = & \color{red}{126x} +18 \color{blue}{-126x} \color{blue}{+70} \\\Leftrightarrow & -525x-126x& = & 18+70 \\\Leftrightarrow & \color{red}{-651} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-651} & & \\\Leftrightarrow & x = \frac{-88}{651} & & \\ & V = \left\{ \frac{-88}{651} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+160} & = & \color{red}{-504x} +49 \\\Leftrightarrow & 1120x \color{red}{+160} \color{blue}{-160} \color{blue}{+504x} & = & \color{red}{-504x} +49 \color{blue}{+504x} \color{blue}{-160} \\\Leftrightarrow & 1120x+504x& = & 49-160 \\\Leftrightarrow & \color{red}{1624} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{1624} & & \\ & V = \left\{ \frac{-111}{1624} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{35}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+105} & = & \color{red}{297x} +88 \\\Leftrightarrow & 462x \color{red}{+105} \color{blue}{-105} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{-105} \\\Leftrightarrow & 462x-297x& = & 88-105 \\\Leftrightarrow & \color{red}{165} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{165} & & \\ & V = \left\{ \frac{-17}{165} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{3})& = & 8x+\frac{4}{7} \\\Leftrightarrow & 15x-\frac{10}{3}& = & 8x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-70} & = & \color{red}{168x} +12 \\\Leftrightarrow & 315x \color{red}{-70} \color{blue}{+70} \color{blue}{-168x} & = & \color{red}{168x} +12 \color{blue}{-168x} \color{blue}{+70} \\\Leftrightarrow & 315x-168x& = & 12+70 \\\Leftrightarrow & \color{red}{147} x& = & 82 \\\Leftrightarrow & x = \frac{82}{147} & & \\ & V = \left\{ \frac{82}{147} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +25 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +25 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 25+84 \\\Leftrightarrow & \color{red}{-245} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-245} & & \\\Leftrightarrow & x = \frac{-109}{245} & & \\ & V = \left\{ \frac{-109}{245} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{7})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 6x-\frac{9}{7}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{36}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-36} & = & \color{red}{140x} +35 \\\Leftrightarrow & 168x \color{red}{-36} \color{blue}{+36} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+36} \\\Leftrightarrow & 168x-140x& = & 35+36 \\\Leftrightarrow & \color{red}{28} x& = & 71 \\\Leftrightarrow & x = \frac{71}{28} & & \\ & V = \left\{ \frac{71}{28} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 270x+105x& = & 50-36 \\\Leftrightarrow & \color{red}{375} x& = & 14 \\\Leftrightarrow & x = \frac{14}{375} & & \\ & V = \left\{ \frac{14}{375} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -2x+\frac{2}{3} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-42x} +14 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+42x} & = & \color{red}{-42x} +14 \color{blue}{+42x} \color{blue}{-90} \\\Leftrightarrow & -378x+42x& = & 14-90 \\\Leftrightarrow & \color{red}{-336} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-336} & & \\\Leftrightarrow & x = \frac{19}{84} & & \\ & V = \left\{ \frac{19}{84} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+6} & = & \color{red}{-21x} +6 \\\Leftrightarrow & 28x \color{red}{+6} \color{blue}{-6} \color{blue}{+21x} & = & \color{red}{-21x} +6 \color{blue}{+21x} \color{blue}{-6} \\\Leftrightarrow & 28x+21x& = & 6-6 \\\Leftrightarrow & \color{red}{49} x& = & 0 \\\Leftrightarrow & x = \frac{0}{49} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -9x-\frac{15}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-189}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -189x \color{red}{-45} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -189x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & -189x+105x& = & 14+45 \\\Leftrightarrow & \color{red}{-84} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-84} & & \\\Leftrightarrow & x = \frac{-59}{84} & & \\ & V = \left\{ \frac{-59}{84} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{140x} +16 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -336x-140x& = & 16+105 \\\Leftrightarrow & \color{red}{-476} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-476} & & \\\Leftrightarrow & x = \frac{-121}{476} & & \\ & V = \left\{ \frac{-121}{476} \right\} & \\\end{align}\)