Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{16}{3}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-112} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 252x \color{red}{-112} \color{blue}{+112} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+112} \\\Leftrightarrow & 252x+105x& = & 18+112 \\\Leftrightarrow & \color{red}{357} x& = & 130 \\\Leftrightarrow & x = \frac{130}{357} & & \\ & V = \left\{ \frac{130}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+88} & = & \color{red}{-891x} +81 \\\Leftrightarrow & -396x \color{red}{+88} \color{blue}{-88} \color{blue}{+891x} & = & \color{red}{-891x} +81 \color{blue}{+891x} \color{blue}{-88} \\\Leftrightarrow & -396x+891x& = & 81-88 \\\Leftrightarrow & \color{red}{495} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{495} & & \\ & V = \left\{ \frac{-7}{495} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-80} & = & \color{red}{-108x} +27 \\\Leftrightarrow & -96x \color{red}{-80} \color{blue}{+80} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+80} \\\Leftrightarrow & -96x+108x& = & 27+80 \\\Leftrightarrow & \color{red}{12} x& = & 107 \\\Leftrightarrow & x = \frac{107}{12} & & \\ & V = \left\{ \frac{107}{12} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{+24} & = & \color{red}{-90x} +15 \\\Leftrightarrow & 200x \color{red}{+24} \color{blue}{-24} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{-24} \\\Leftrightarrow & 200x+90x& = & 15-24 \\\Leftrightarrow & \color{red}{290} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{290} & & \\ & V = \left\{ \frac{-9}{290} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{20}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-40} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 72x \color{red}{-40} \color{blue}{+40} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{+40} \\\Leftrightarrow & 72x+30x& = & 9+40 \\\Leftrightarrow & \color{red}{102} x& = & 49 \\\Leftrightarrow & x = \frac{49}{102} & & \\ & V = \left\{ \frac{49}{102} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{2})& = & -3x+\frac{3}{5} \\\Leftrightarrow & 28x+\frac{35}{2}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{+175} & = & \color{red}{-30x} +6 \\\Leftrightarrow & 280x \color{red}{+175} \color{blue}{-175} \color{blue}{+30x} & = & \color{red}{-30x} +6 \color{blue}{+30x} \color{blue}{-175} \\\Leftrightarrow & 280x+30x& = & 6-175 \\\Leftrightarrow & \color{red}{310} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{310} & & \\ & V = \left\{ \frac{-169}{310} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{720}{ \color{blue}{30} }x+ \frac{144}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{-210x} +25 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{+210x} & = & \color{red}{-210x} +25 \color{blue}{+210x} \color{blue}{-144} \\\Leftrightarrow & 720x+210x& = & 25-144 \\\Leftrightarrow & \color{red}{930} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{930} & & \\ & V = \left\{ \frac{-119}{930} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{12})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{25}{12}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1980}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{-264}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1980x \color{red}{-275} & = & \color{red}{-264x} +72 \\\Leftrightarrow & 1980x \color{red}{-275} \color{blue}{+275} \color{blue}{+264x} & = & \color{red}{-264x} +72 \color{blue}{+264x} \color{blue}{+275} \\\Leftrightarrow & 1980x+264x& = & 72+275 \\\Leftrightarrow & \color{red}{2244} x& = & 347 \\\Leftrightarrow & x = \frac{347}{2244} & & \\ & V = \left\{ \frac{347}{2244} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & -8x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{12}{11}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-12} & = & \color{red}{-88x} +10 \\\Leftrightarrow & 165x \color{red}{-12} \color{blue}{+12} \color{blue}{+88x} & = & \color{red}{-88x} +10 \color{blue}{+88x} \color{blue}{+12} \\\Leftrightarrow & 165x+88x& = & 10+12 \\\Leftrightarrow & \color{red}{253} x& = & 22 \\\Leftrightarrow & x = \frac{22}{253} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{-245x} +20 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 525x+245x& = & 20+84 \\\Leftrightarrow & \color{red}{770} x& = & 104 \\\Leftrightarrow & x = \frac{104}{770} & & \\\Leftrightarrow & x = \frac{52}{385} & & \\ & V = \left\{ \frac{52}{385} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +25 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 25-24 \\\Leftrightarrow & \color{red}{70} x& = & 1 \\\Leftrightarrow & x = \frac{1}{70} & & \\ & V = \left\{ \frac{1}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-84} & = & \color{red}{-105x} +25 \\\Leftrightarrow & 280x \color{red}{-84} \color{blue}{+84} \color{blue}{+105x} & = & \color{red}{-105x} +25 \color{blue}{+105x} \color{blue}{+84} \\\Leftrightarrow & 280x+105x& = & 25+84 \\\Leftrightarrow & \color{red}{385} x& = & 109 \\\Leftrightarrow & x = \frac{109}{385} & & \\ & V = \left\{ \frac{109}{385} \right\} & \\\end{align}\)