Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{-189x} +12 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{+189x} & = & \color{red}{-189x} +12 \color{blue}{+189x} \color{blue}{+140} \\\Leftrightarrow & 420x+189x& = & 12+140 \\\Leftrightarrow & \color{red}{609} x& = & 152 \\\Leftrightarrow & x = \frac{152}{609} & & \\ & V = \left\{ \frac{152}{609} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+48} & = & \color{red}{105x} +28 \\\Leftrightarrow & -252x \color{red}{+48} \color{blue}{-48} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-48} \\\Leftrightarrow & -252x-105x& = & 28-48 \\\Leftrightarrow & \color{red}{-357} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-357} & & \\\Leftrightarrow & x = \frac{20}{357} & & \\ & V = \left\{ \frac{20}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{9}{8} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-352}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -352x \color{red}{+80} & = & \color{red}{792x} +99 \\\Leftrightarrow & -352x \color{red}{+80} \color{blue}{-80} \color{blue}{-792x} & = & \color{red}{792x} +99 \color{blue}{-792x} \color{blue}{-80} \\\Leftrightarrow & -352x-792x& = & 99-80 \\\Leftrightarrow & \color{red}{-1144} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-1144} & & \\\Leftrightarrow & x = \frac{-19}{1144} & & \\ & V = \left\{ \frac{-19}{1144} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+98} & = & \color{red}{-189x} +27 \\\Leftrightarrow & -735x \color{red}{+98} \color{blue}{-98} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{-98} \\\Leftrightarrow & -735x+189x& = & 27-98 \\\Leftrightarrow & \color{red}{-546} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-546} & & \\\Leftrightarrow & x = \frac{71}{546} & & \\ & V = \left\{ \frac{71}{546} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -9x-\frac{6}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-42} & = & \color{red}{-175x} +30 \\\Leftrightarrow & -315x \color{red}{-42} \color{blue}{+42} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{+42} \\\Leftrightarrow & -315x+175x& = & 30+42 \\\Leftrightarrow & \color{red}{-140} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-140} & & \\\Leftrightarrow & x = \frac{-18}{35} & & \\ & V = \left\{ \frac{-18}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{385x} +30 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1650x-385x& = & 30+264 \\\Leftrightarrow & \color{red}{1265} x& = & 294 \\\Leftrightarrow & x = \frac{294}{1265} & & \\ & V = \left\{ \frac{294}{1265} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{12}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+108} & = & \color{red}{693x} +44 \\\Leftrightarrow & -1980x \color{red}{+108} \color{blue}{-108} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-108} \\\Leftrightarrow & -1980x-693x& = & 44-108 \\\Leftrightarrow & \color{red}{-2673} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-2673} & & \\\Leftrightarrow & x = \frac{64}{2673} & & \\ & V = \left\{ \frac{64}{2673} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{539x} +110 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-126} \\\Leftrightarrow & 2310x-539x& = & 110-126 \\\Leftrightarrow & \color{red}{1771} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{1771} & & \\ & V = \left\{ \frac{-16}{1771} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{10}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-110} & = & \color{red}{-891x} +54 \\\Leftrightarrow & 396x \color{red}{-110} \color{blue}{+110} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{+110} \\\Leftrightarrow & 396x+891x& = & 54+110 \\\Leftrightarrow & \color{red}{1287} x& = & 164 \\\Leftrightarrow & x = \frac{164}{1287} & & \\ & V = \left\{ \frac{164}{1287} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-100} & = & \color{red}{-175x} +14 \\\Leftrightarrow & -420x \color{red}{-100} \color{blue}{+100} \color{blue}{+175x} & = & \color{red}{-175x} +14 \color{blue}{+175x} \color{blue}{+100} \\\Leftrightarrow & -420x+175x& = & 14+100 \\\Leftrightarrow & \color{red}{-245} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-245} & & \\\Leftrightarrow & x = \frac{-114}{245} & & \\ & V = \left\{ \frac{-114}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{12})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{25}{12}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+25} & = & \color{red}{96x} +54 \\\Leftrightarrow & 180x \color{red}{+25} \color{blue}{-25} \color{blue}{-96x} & = & \color{red}{96x} +54 \color{blue}{-96x} \color{blue}{-25} \\\Leftrightarrow & 180x-96x& = & 54-25 \\\Leftrightarrow & \color{red}{84} x& = & 29 \\\Leftrightarrow & x = \frac{29}{84} & & \\ & V = \left\{ \frac{29}{84} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-70} & = & \color{red}{539x} +66 \\\Leftrightarrow & -1540x \color{red}{-70} \color{blue}{+70} \color{blue}{-539x} & = & \color{red}{539x} +66 \color{blue}{-539x} \color{blue}{+70} \\\Leftrightarrow & -1540x-539x& = & 66+70 \\\Leftrightarrow & \color{red}{-2079} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-2079} & & \\\Leftrightarrow & x = \frac{-136}{2079} & & \\ & V = \left\{ \frac{-136}{2079} \right\} & \\\end{align}\)