Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -25x-\frac{15}{2}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-60} & = & \color{red}{-56x} +5 \\\Leftrightarrow & -200x \color{red}{-60} \color{blue}{+60} \color{blue}{+56x} & = & \color{red}{-56x} +5 \color{blue}{+56x} \color{blue}{+60} \\\Leftrightarrow & -200x+56x& = & 5+60 \\\Leftrightarrow & \color{red}{-144} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-144} & & \\\Leftrightarrow & x = \frac{-65}{144} & & \\ & V = \left\{ \frac{-65}{144} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+80} & = & \color{red}{168x} +49 \\\Leftrightarrow & -1120x \color{red}{+80} \color{blue}{-80} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{-80} \\\Leftrightarrow & -1120x-168x& = & 49-80 \\\Leftrightarrow & \color{red}{-1288} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1288} & & \\\Leftrightarrow & x = \frac{31}{1288} & & \\ & V = \left\{ \frac{31}{1288} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{12})& = & -6x+\frac{4}{11} \\\Leftrightarrow & -28x+\frac{35}{12}& = & -6x+\frac{4}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3696}{ \color{blue}{132} }x+ \frac{385}{ \color{blue}{132} })& = & (\frac{-792}{ \color{blue}{132} }x+ \frac{48}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3696x \color{red}{+385} & = & \color{red}{-792x} +48 \\\Leftrightarrow & -3696x \color{red}{+385} \color{blue}{-385} \color{blue}{+792x} & = & \color{red}{-792x} +48 \color{blue}{+792x} \color{blue}{-385} \\\Leftrightarrow & -3696x+792x& = & 48-385 \\\Leftrightarrow & \color{red}{-2904} x& = & -337 \\\Leftrightarrow & x = \frac{-337}{-2904} & & \\\Leftrightarrow & x = \frac{337}{2904} & & \\ & V = \left\{ \frac{337}{2904} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -9x+\frac{5}{8} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-576}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -576x \color{red}{-64} & = & \color{red}{-648x} +45 \\\Leftrightarrow & -576x \color{red}{-64} \color{blue}{+64} \color{blue}{+648x} & = & \color{red}{-648x} +45 \color{blue}{+648x} \color{blue}{+64} \\\Leftrightarrow & -576x+648x& = & 45+64 \\\Leftrightarrow & \color{red}{72} x& = & 109 \\\Leftrightarrow & x = \frac{109}{72} & & \\ & V = \left\{ \frac{109}{72} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{9})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{25}{9}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-275} & = & \color{red}{693x} +90 \\\Leftrightarrow & -1980x \color{red}{-275} \color{blue}{+275} \color{blue}{-693x} & = & \color{red}{693x} +90 \color{blue}{-693x} \color{blue}{+275} \\\Leftrightarrow & -1980x-693x& = & 90+275 \\\Leftrightarrow & \color{red}{-2673} x& = & 365 \\\Leftrightarrow & x = \frac{365}{-2673} & & \\\Leftrightarrow & x = \frac{-365}{2673} & & \\ & V = \left\{ \frac{-365}{2673} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{15}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-135} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 945x \color{red}{-135} \color{blue}{+135} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+135} \\\Leftrightarrow & 945x+441x& = & 70+135 \\\Leftrightarrow & \color{red}{1386} x& = & 205 \\\Leftrightarrow & x = \frac{205}{1386} & & \\ & V = \left\{ \frac{205}{1386} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+120} & = & \color{red}{275x} +88 \\\Leftrightarrow & 990x \color{red}{+120} \color{blue}{-120} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{-120} \\\Leftrightarrow & 990x-275x& = & 88-120 \\\Leftrightarrow & \color{red}{715} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{715} & & \\ & V = \left\{ \frac{-32}{715} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 1320x+275x& = & 50+132 \\\Leftrightarrow & \color{red}{1595} x& = & 182 \\\Leftrightarrow & x = \frac{182}{1595} & & \\ & V = \left\{ \frac{182}{1595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-42} & = & \color{red}{81x} +10 \\\Leftrightarrow & 252x \color{red}{-42} \color{blue}{+42} \color{blue}{-81x} & = & \color{red}{81x} +10 \color{blue}{-81x} \color{blue}{+42} \\\Leftrightarrow & 252x-81x& = & 10+42 \\\Leftrightarrow & \color{red}{171} x& = & 52 \\\Leftrightarrow & x = \frac{52}{171} & & \\ & V = \left\{ \frac{52}{171} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 4x+\frac{3}{4} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{112}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-40} & = & \color{red}{112x} +21 \\\Leftrightarrow & -420x \color{red}{-40} \color{blue}{+40} \color{blue}{-112x} & = & \color{red}{112x} +21 \color{blue}{-112x} \color{blue}{+40} \\\Leftrightarrow & -420x-112x& = & 21+40 \\\Leftrightarrow & \color{red}{-532} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-532} & & \\\Leftrightarrow & x = \frac{-61}{532} & & \\ & V = \left\{ \frac{-61}{532} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-90} & = & \color{red}{105x} +70 \\\Leftrightarrow & -252x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & -252x-105x& = & 70+90 \\\Leftrightarrow & \color{red}{-357} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-357} & & \\\Leftrightarrow & x = \frac{-160}{357} & & \\ & V = \left\{ \frac{-160}{357} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{-16} & = & \color{red}{-90x} +81 \\\Leftrightarrow & 108x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +81 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & 108x+90x& = & 81+16 \\\Leftrightarrow & \color{red}{198} x& = & 97 \\\Leftrightarrow & x = \frac{97}{198} & & \\ & V = \left\{ \frac{97}{198} \right\} & \\\end{align}\)