Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{10}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-30} \\\Leftrightarrow & 126x+105x& = & 70-30 \\\Leftrightarrow & \color{red}{231} x& = & 40 \\\Leftrightarrow & x = \frac{40}{231} & & \\ & V = \left\{ \frac{40}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+108} & = & \color{red}{225x} +10 \\\Leftrightarrow & -1080x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -1080x-225x& = & 10-108 \\\Leftrightarrow & \color{red}{-1305} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-1305} & & \\\Leftrightarrow & x = \frac{98}{1305} & & \\ & V = \left\{ \frac{98}{1305} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1568x \color{red}{+147} & = & \color{red}{-504x} +24 \\\Leftrightarrow & -1568x \color{red}{+147} \color{blue}{-147} \color{blue}{+504x} & = & \color{red}{-504x} +24 \color{blue}{+504x} \color{blue}{-147} \\\Leftrightarrow & -1568x+504x& = & 24-147 \\\Leftrightarrow & \color{red}{-1064} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-1064} & & \\\Leftrightarrow & x = \frac{123}{1064} & & \\ & V = \left\{ \frac{123}{1064} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 14x-\frac{35}{2}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x- \frac{210}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{-210} & = & \color{red}{-36x} +5 \\\Leftrightarrow & 168x \color{red}{-210} \color{blue}{+210} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{+210} \\\Leftrightarrow & 168x+36x& = & 5+210 \\\Leftrightarrow & \color{red}{204} x& = & 215 \\\Leftrightarrow & x = \frac{215}{204} & & \\ & V = \left\{ \frac{215}{204} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 30x-\frac{30}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1980}{ \color{blue}{66} }x- \frac{180}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1980x \color{red}{-180} & = & \color{red}{-462x} +77 \\\Leftrightarrow & 1980x \color{red}{-180} \color{blue}{+180} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{+180} \\\Leftrightarrow & 1980x+462x& = & 77+180 \\\Leftrightarrow & \color{red}{2442} x& = & 257 \\\Leftrightarrow & x = \frac{257}{2442} & & \\ & V = \left\{ \frac{257}{2442} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & 4x+\frac{5}{11} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-308} & = & \color{red}{396x} +45 \\\Leftrightarrow & -2772x \color{red}{-308} \color{blue}{+308} \color{blue}{-396x} & = & \color{red}{396x} +45 \color{blue}{-396x} \color{blue}{+308} \\\Leftrightarrow & -2772x-396x& = & 45+308 \\\Leftrightarrow & \color{red}{-3168} x& = & 353 \\\Leftrightarrow & x = \frac{353}{-3168} & & \\\Leftrightarrow & x = \frac{-353}{3168} & & \\ & V = \left\{ \frac{-353}{3168} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 42+50 \\\Leftrightarrow & \color{red}{-105} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-105} & & \\\Leftrightarrow & x = \frac{-92}{105} & & \\ & V = \left\{ \frac{-92}{105} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{75x} +50 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 270x-75x& = & 50+72 \\\Leftrightarrow & \color{red}{195} x& = & 122 \\\Leftrightarrow & x = \frac{122}{195} & & \\ & V = \left\{ \frac{122}{195} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+110} \\\Leftrightarrow & -308x+385x& = & 35+110 \\\Leftrightarrow & \color{red}{77} x& = & 145 \\\Leftrightarrow & x = \frac{145}{77} & & \\ & V = \left\{ \frac{145}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & 120x+42x& = & 21-40 \\\Leftrightarrow & \color{red}{162} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{162} & & \\ & V = \left\{ \frac{-19}{162} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{3})& = & -9x+\frac{5}{4} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x+ \frac{112}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{+112} & = & \color{red}{-108x} +15 \\\Leftrightarrow & 336x \color{red}{+112} \color{blue}{-112} \color{blue}{+108x} & = & \color{red}{-108x} +15 \color{blue}{+108x} \color{blue}{-112} \\\Leftrightarrow & 336x+108x& = & 15-112 \\\Leftrightarrow & \color{red}{444} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{444} & & \\ & V = \left\{ \frac{-97}{444} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{360x} +36 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-360x} & = & \color{red}{360x} +36 \color{blue}{-360x} \color{blue}{-105} \\\Leftrightarrow & -1400x-360x& = & 36-105 \\\Leftrightarrow & \color{red}{-1760} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-1760} & & \\\Leftrightarrow & x = \frac{69}{1760} & & \\ & V = \left\{ \frac{69}{1760} \right\} & \\\end{align}\)