Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+72} & = & \color{red}{231x} +55 \\\Leftrightarrow & 990x \color{red}{+72} \color{blue}{-72} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{-72} \\\Leftrightarrow & 990x-231x& = & 55-72 \\\Leftrightarrow & \color{red}{759} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{759} & & \\ & V = \left\{ \frac{-17}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{-115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-115} & & \\\Leftrightarrow & x = \frac{-18}{115} & & \\ & V = \left\{ \frac{-18}{115} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -4x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-40x} +45 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+40x} & = & \color{red}{-40x} +45 \color{blue}{+40x} \color{blue}{-24} \\\Leftrightarrow & 150x+40x& = & 45-24 \\\Leftrightarrow & \color{red}{190} x& = & 21 \\\Leftrightarrow & x = \frac{21}{190} & & \\ & V = \left\{ \frac{21}{190} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{+108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 720x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & 720x+225x& = & 40-108 \\\Leftrightarrow & \color{red}{945} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{945} & & \\ & V = \left\{ \frac{-68}{945} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{-20} & = & \color{red}{27x} +8 \\\Leftrightarrow & -75x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & -75x-27x& = & 8+20 \\\Leftrightarrow & \color{red}{-102} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-102} & & \\\Leftrightarrow & x = \frac{-14}{51} & & \\ & V = \left\{ \frac{-14}{51} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{8}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-24} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -330x \color{red}{-24} \color{blue}{+24} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+24} \\\Leftrightarrow & -330x+231x& = & 44+24 \\\Leftrightarrow & \color{red}{-99} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-99} & & \\\Leftrightarrow & x = \frac{-68}{99} & & \\ & V = \left\{ \frac{-68}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{12})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 10x+\frac{25}{12}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+25} & = & \color{red}{84x} +21 \\\Leftrightarrow & 120x \color{red}{+25} \color{blue}{-25} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{-25} \\\Leftrightarrow & 120x-84x& = & 21-25 \\\Leftrightarrow & \color{red}{36} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{36} & & \\\Leftrightarrow & x = \frac{-1}{9} & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{2})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -6x-\frac{15}{2}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-105} & = & \color{red}{-98x} +6 \\\Leftrightarrow & -84x \color{red}{-105} \color{blue}{+105} \color{blue}{+98x} & = & \color{red}{-98x} +6 \color{blue}{+98x} \color{blue}{+105} \\\Leftrightarrow & -84x+98x& = & 6+105 \\\Leftrightarrow & \color{red}{14} x& = & 111 \\\Leftrightarrow & x = \frac{111}{14} & & \\ & V = \left\{ \frac{111}{14} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-8} \\\Leftrightarrow & -60x+70x& = & 3-8 \\\Leftrightarrow & \color{red}{10} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{10} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{-72} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 1320x \color{red}{-72} \color{blue}{+72} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+72} \\\Leftrightarrow & 1320x+308x& = & 99+72 \\\Leftrightarrow & \color{red}{1628} x& = & 171 \\\Leftrightarrow & x = \frac{171}{1628} & & \\ & V = \left\{ \frac{171}{1628} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{-42x} +63 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +63 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & 140x+42x& = & 63-20 \\\Leftrightarrow & \color{red}{182} x& = & 43 \\\Leftrightarrow & x = \frac{43}{182} & & \\ & V = \left\{ \frac{43}{182} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{11})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x-\frac{4}{11}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-28} & = & \color{red}{539x} +22 \\\Leftrightarrow & -770x \color{red}{-28} \color{blue}{+28} \color{blue}{-539x} & = & \color{red}{539x} +22 \color{blue}{-539x} \color{blue}{+28} \\\Leftrightarrow & -770x-539x& = & 22+28 \\\Leftrightarrow & \color{red}{-1309} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-1309} & & \\\Leftrightarrow & x = \frac{-50}{1309} & & \\ & V = \left\{ \frac{-50}{1309} \right\} & \\\end{align}\)