Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{2})& = & -6x+\frac{9}{4} \\\Leftrightarrow & -35x-\frac{35}{2}& = & -6x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-140}{ \color{blue}{4} }x- \frac{70}{ \color{blue}{4} })& = & (\frac{-24}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -140x \color{red}{-70} & = & \color{red}{-24x} +9 \\\Leftrightarrow & -140x \color{red}{-70} \color{blue}{+70} \color{blue}{+24x} & = & \color{red}{-24x} +9 \color{blue}{+24x} \color{blue}{+70} \\\Leftrightarrow & -140x+24x& = & 9+70 \\\Leftrightarrow & \color{red}{-116} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-116} & & \\\Leftrightarrow & x = \frac{-79}{116} & & \\ & V = \left\{ \frac{-79}{116} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-110} & = & \color{red}{539x} +70 \\\Leftrightarrow & -462x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -462x-539x& = & 70+110 \\\Leftrightarrow & \color{red}{-1001} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-1001} & & \\\Leftrightarrow & x = \frac{-180}{1001} & & \\ & V = \left\{ \frac{-180}{1001} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 4x+\frac{8}{5} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-9} & = & \color{red}{20x} +8 \\\Leftrightarrow & 45x \color{red}{-9} \color{blue}{+9} \color{blue}{-20x} & = & \color{red}{20x} +8 \color{blue}{-20x} \color{blue}{+9} \\\Leftrightarrow & 45x-20x& = & 8+9 \\\Leftrightarrow & \color{red}{25} x& = & 17 \\\Leftrightarrow & x = \frac{17}{25} & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -2x+\frac{2}{9} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{-54} & = & \color{red}{-126x} +14 \\\Leftrightarrow & 567x \color{red}{-54} \color{blue}{+54} \color{blue}{+126x} & = & \color{red}{-126x} +14 \color{blue}{+126x} \color{blue}{+54} \\\Leftrightarrow & 567x+126x& = & 14+54 \\\Leftrightarrow & \color{red}{693} x& = & 68 \\\Leftrightarrow & x = \frac{68}{693} & & \\ & V = \left\{ \frac{68}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{9}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-27} \\\Leftrightarrow & 180x+75x& = & 20-27 \\\Leftrightarrow & \color{red}{255} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{255} & & \\ & V = \left\{ \frac{-7}{255} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+72} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -180x+75x& = & 20-72 \\\Leftrightarrow & \color{red}{-105} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-105} & & \\\Leftrightarrow & x = \frac{52}{105} & & \\ & V = \left\{ \frac{52}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{+96} & = & \color{red}{294x} +49 \\\Leftrightarrow & -840x \color{red}{+96} \color{blue}{-96} \color{blue}{-294x} & = & \color{red}{294x} +49 \color{blue}{-294x} \color{blue}{-96} \\\Leftrightarrow & -840x-294x& = & 49-96 \\\Leftrightarrow & \color{red}{-1134} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-1134} & & \\\Leftrightarrow & x = \frac{47}{1134} & & \\ & V = \left\{ \frac{47}{1134} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{11})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -4x-\frac{8}{11}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-40} & = & \color{red}{495x} +44 \\\Leftrightarrow & -220x \color{red}{-40} \color{blue}{+40} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{+40} \\\Leftrightarrow & -220x-495x& = & 44+40 \\\Leftrightarrow & \color{red}{-715} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-715} & & \\\Leftrightarrow & x = \frac{-84}{715} & & \\ & V = \left\{ \frac{-84}{715} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+180} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1320x \color{red}{+180} \color{blue}{-180} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-180} \\\Leftrightarrow & 1320x-550x& = & 99-180 \\\Leftrightarrow & \color{red}{770} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{770} & & \\ & V = \left\{ \frac{-81}{770} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-135x} +20 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{-12} \\\Leftrightarrow & 60x+135x& = & 20-12 \\\Leftrightarrow & \color{red}{195} x& = & 8 \\\Leftrightarrow & x = \frac{8}{195} & & \\ & V = \left\{ \frac{8}{195} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{6}{7}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-54} & = & \color{red}{504x} +70 \\\Leftrightarrow & -945x \color{red}{-54} \color{blue}{+54} \color{blue}{-504x} & = & \color{red}{504x} +70 \color{blue}{-504x} \color{blue}{+54} \\\Leftrightarrow & -945x-504x& = & 70+54 \\\Leftrightarrow & \color{red}{-1449} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-1449} & & \\\Leftrightarrow & x = \frac{-124}{1449} & & \\ & V = \left\{ \frac{-124}{1449} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-72} & = & \color{red}{75x} +50 \\\Leftrightarrow & 180x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 180x-75x& = & 50+72 \\\Leftrightarrow & \color{red}{105} x& = & 122 \\\Leftrightarrow & x = \frac{122}{105} & & \\ & V = \left\{ \frac{122}{105} \right\} & \\\end{align}\)