Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{4}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-360}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -360x \color{red}{+40} & = & \color{red}{810x} +27 \\\Leftrightarrow & -360x \color{red}{+40} \color{blue}{-40} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{-40} \\\Leftrightarrow & -360x-810x& = & 27-40 \\\Leftrightarrow & \color{red}{-1170} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-1170} & & \\\Leftrightarrow & x = \frac{1}{90} & & \\ & V = \left\{ \frac{1}{90} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{165x} +6 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{-165x} & = & \color{red}{165x} +6 \color{blue}{-165x} \color{blue}{-154} \\\Leftrightarrow & 924x-165x& = & 6-154 \\\Leftrightarrow & \color{red}{759} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{759} & & \\ & V = \left\{ \frac{-148}{759} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{11})& = & 2x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{6}{11}& = & 2x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+42} & = & \color{red}{154x} +44 \\\Leftrightarrow & 693x \color{red}{+42} \color{blue}{-42} \color{blue}{-154x} & = & \color{red}{154x} +44 \color{blue}{-154x} \color{blue}{-42} \\\Leftrightarrow & 693x-154x& = & 44-42 \\\Leftrightarrow & \color{red}{539} x& = & 2 \\\Leftrightarrow & x = \frac{2}{539} & & \\ & V = \left\{ \frac{2}{539} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 30x+\frac{30}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{231x} +44 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-90} \\\Leftrightarrow & 990x-231x& = & 44-90 \\\Leftrightarrow & \color{red}{759} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{759} & & \\\Leftrightarrow & x = \frac{-2}{33} & & \\ & V = \left\{ \frac{-2}{33} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+12} & = & \color{red}{-126x} +21 \\\Leftrightarrow & 112x \color{red}{+12} \color{blue}{-12} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-12} \\\Leftrightarrow & 112x+126x& = & 21-12 \\\Leftrightarrow & \color{red}{238} x& = & 9 \\\Leftrightarrow & x = \frac{9}{238} & & \\ & V = \left\{ \frac{9}{238} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1680}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1680x \color{red}{-300} & = & \color{red}{350x} +63 \\\Leftrightarrow & -1680x \color{red}{-300} \color{blue}{+300} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{+300} \\\Leftrightarrow & -1680x-350x& = & 63+300 \\\Leftrightarrow & \color{red}{-2030} x& = & 363 \\\Leftrightarrow & x = \frac{363}{-2030} & & \\\Leftrightarrow & x = \frac{-363}{2030} & & \\ & V = \left\{ \frac{-363}{2030} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-50} & = & \color{red}{385x} +88 \\\Leftrightarrow & 440x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & 440x-385x& = & 88+50 \\\Leftrightarrow & \color{red}{55} x& = & 138 \\\Leftrightarrow & x = \frac{138}{55} & & \\ & V = \left\{ \frac{138}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{6})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{35}{6}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{-175} & = & \color{red}{240x} +36 \\\Leftrightarrow & -630x \color{red}{-175} \color{blue}{+175} \color{blue}{-240x} & = & \color{red}{240x} +36 \color{blue}{-240x} \color{blue}{+175} \\\Leftrightarrow & -630x-240x& = & 36+175 \\\Leftrightarrow & \color{red}{-870} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-870} & & \\\Leftrightarrow & x = \frac{-211}{870} & & \\ & V = \left\{ \frac{-211}{870} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{8})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{15}{8}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{+45} & = & \color{red}{-72x} +64 \\\Leftrightarrow & 480x \color{red}{+45} \color{blue}{-45} \color{blue}{+72x} & = & \color{red}{-72x} +64 \color{blue}{+72x} \color{blue}{-45} \\\Leftrightarrow & 480x+72x& = & 64-45 \\\Leftrightarrow & \color{red}{552} x& = & 19 \\\Leftrightarrow & x = \frac{19}{552} & & \\ & V = \left\{ \frac{19}{552} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -8x-\frac{4}{5}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-44} & = & \color{red}{-165x} +40 \\\Leftrightarrow & -440x \color{red}{-44} \color{blue}{+44} \color{blue}{+165x} & = & \color{red}{-165x} +40 \color{blue}{+165x} \color{blue}{+44} \\\Leftrightarrow & -440x+165x& = & 40+44 \\\Leftrightarrow & \color{red}{-275} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-275} & & \\\Leftrightarrow & x = \frac{-84}{275} & & \\ & V = \left\{ \frac{-84}{275} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -540x+225x& = & 10-108 \\\Leftrightarrow & \color{red}{-315} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-315} & & \\\Leftrightarrow & x = \frac{14}{45} & & \\ & V = \left\{ \frac{14}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-6} & = & \color{red}{14x} +10 \\\Leftrightarrow & 105x \color{red}{-6} \color{blue}{+6} \color{blue}{-14x} & = & \color{red}{14x} +10 \color{blue}{-14x} \color{blue}{+6} \\\Leftrightarrow & 105x-14x& = & 10+6 \\\Leftrightarrow & \color{red}{91} x& = & 16 \\\Leftrightarrow & x = \frac{16}{91} & & \\ & V = \left\{ \frac{16}{91} \right\} & \\\end{align}\)