Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{8}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-40} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 880x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & 880x+385x& = & 66+40 \\\Leftrightarrow & \color{red}{1265} x& = & 106 \\\Leftrightarrow & x = \frac{106}{1265} & & \\ & V = \left\{ \frac{106}{1265} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{154x} +55 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{-24} \\\Leftrightarrow & -132x-154x& = & 55-24 \\\Leftrightarrow & \color{red}{-286} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-286} & & \\\Leftrightarrow & x = \frac{-31}{286} & & \\ & V = \left\{ \frac{-31}{286} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{2})& = & 4x+\frac{9}{7} \\\Leftrightarrow & -15x+\frac{25}{2}& = & 4x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{56}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+175} & = & \color{red}{56x} +18 \\\Leftrightarrow & -210x \color{red}{+175} \color{blue}{-175} \color{blue}{-56x} & = & \color{red}{56x} +18 \color{blue}{-56x} \color{blue}{-175} \\\Leftrightarrow & -210x-56x& = & 18-175 \\\Leftrightarrow & \color{red}{-266} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-266} & & \\\Leftrightarrow & x = \frac{157}{266} & & \\ & V = \left\{ \frac{157}{266} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{35x} +8 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & 84x-35x& = & 8+30 \\\Leftrightarrow & \color{red}{49} x& = & 38 \\\Leftrightarrow & x = \frac{38}{49} & & \\ & V = \left\{ \frac{38}{49} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-24} & = & \color{red}{-40x} +15 \\\Leftrightarrow & -150x \color{red}{-24} \color{blue}{+24} \color{blue}{+40x} & = & \color{red}{-40x} +15 \color{blue}{+40x} \color{blue}{+24} \\\Leftrightarrow & -150x+40x& = & 15+24 \\\Leftrightarrow & \color{red}{-110} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-110} & & \\\Leftrightarrow & x = \frac{-39}{110} & & \\ & V = \left\{ \frac{-39}{110} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{9})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 20x+\frac{20}{9}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{-126x} +63 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{-40} \\\Leftrightarrow & 360x+126x& = & 63-40 \\\Leftrightarrow & \color{red}{486} x& = & 23 \\\Leftrightarrow & x = \frac{23}{486} & & \\ & V = \left\{ \frac{23}{486} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{4})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 9x+\frac{9}{4}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{36}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 36x \color{red}{+9} & = & \color{red}{-28x} +7 \\\Leftrightarrow & 36x \color{red}{+9} \color{blue}{-9} \color{blue}{+28x} & = & \color{red}{-28x} +7 \color{blue}{+28x} \color{blue}{-9} \\\Leftrightarrow & 36x+28x& = & 7-9 \\\Leftrightarrow & \color{red}{64} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{64} & & \\\Leftrightarrow & x = \frac{-1}{32} & & \\ & V = \left\{ \frac{-1}{32} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{6})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -20x-\frac{25}{6}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{18}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{-125} & = & \color{red}{210x} +18 \\\Leftrightarrow & -600x \color{red}{-125} \color{blue}{+125} \color{blue}{-210x} & = & \color{red}{210x} +18 \color{blue}{-210x} \color{blue}{+125} \\\Leftrightarrow & -600x-210x& = & 18+125 \\\Leftrightarrow & \color{red}{-810} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-810} & & \\\Leftrightarrow & x = \frac{-143}{810} & & \\ & V = \left\{ \frac{-143}{810} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{14}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{42}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-42} & = & \color{red}{165x} +44 \\\Leftrightarrow & -924x \color{red}{-42} \color{blue}{+42} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+42} \\\Leftrightarrow & -924x-165x& = & 44+42 \\\Leftrightarrow & \color{red}{-1089} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-1089} & & \\\Leftrightarrow & x = \frac{-86}{1089} & & \\ & V = \left\{ \frac{-86}{1089} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{8}{7}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+88} & = & \color{red}{231x} +14 \\\Leftrightarrow & 770x \color{red}{+88} \color{blue}{-88} \color{blue}{-231x} & = & \color{red}{231x} +14 \color{blue}{-231x} \color{blue}{-88} \\\Leftrightarrow & 770x-231x& = & 14-88 \\\Leftrightarrow & \color{red}{539} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{539} & & \\ & V = \left\{ \frac{-74}{539} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & 8x+\frac{9}{7} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+196} & = & \color{red}{168x} +27 \\\Leftrightarrow & -441x \color{red}{+196} \color{blue}{-196} \color{blue}{-168x} & = & \color{red}{168x} +27 \color{blue}{-168x} \color{blue}{-196} \\\Leftrightarrow & -441x-168x& = & 27-196 \\\Leftrightarrow & \color{red}{-609} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-609} & & \\\Leftrightarrow & x = \frac{169}{609} & & \\ & V = \left\{ \frac{169}{609} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-40} & = & \color{red}{30x} +27 \\\Leftrightarrow & -150x \color{red}{-40} \color{blue}{+40} \color{blue}{-30x} & = & \color{red}{30x} +27 \color{blue}{-30x} \color{blue}{+40} \\\Leftrightarrow & -150x-30x& = & 27+40 \\\Leftrightarrow & \color{red}{-180} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-180} & & \\\Leftrightarrow & x = \frac{-67}{180} & & \\ & V = \left\{ \frac{-67}{180} \right\} & \\\end{align}\)