Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & 720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{420} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{420} & & \\ & V = \left\{ \frac{-109}{420} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-4} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+4} \\\Leftrightarrow & 20x+25x& = & 6+4 \\\Leftrightarrow & \color{red}{45} x& = & 10 \\\Leftrightarrow & x = \frac{10}{45} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+4} & = & \color{red}{9x} +2 \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-4} \\\Leftrightarrow & 24x-9x& = & 2-4 \\\Leftrightarrow & \color{red}{15} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-10} & = & \color{red}{-21x} +3 \\\Leftrightarrow & -140x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & -140x+21x& = & 3+10 \\\Leftrightarrow & \color{red}{-119} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-119} & & \\\Leftrightarrow & x = \frac{-13}{119} & & \\ & V = \left\{ \frac{-13}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{360}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 360x \color{red}{-80} & = & \color{red}{270x} +81 \\\Leftrightarrow & 360x \color{red}{-80} \color{blue}{+80} \color{blue}{-270x} & = & \color{red}{270x} +81 \color{blue}{-270x} \color{blue}{+80} \\\Leftrightarrow & 360x-270x& = & 81+80 \\\Leftrightarrow & \color{red}{90} x& = & 161 \\\Leftrightarrow & x = \frac{161}{90} & & \\ & V = \left\{ \frac{161}{90} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{9})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{315x} +63 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & 180x-315x& = & 63+40 \\\Leftrightarrow & \color{red}{-135} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-135} & & \\\Leftrightarrow & x = \frac{-103}{135} & & \\ & V = \left\{ \frac{-103}{135} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +35 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 35-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1001} & & \\\Leftrightarrow & x = \frac{31}{1001} & & \\ & V = \left\{ \frac{31}{1001} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -10x+\frac{20}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+180} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -630x \color{red}{+180} \color{blue}{-180} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{-180} \\\Leftrightarrow & -630x+441x& = & 49-180 \\\Leftrightarrow & \color{red}{-189} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-189} & & \\\Leftrightarrow & x = \frac{131}{189} & & \\ & V = \left\{ \frac{131}{189} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{1}{2})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 25x-\frac{5}{2}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{55}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-55} & = & \color{red}{-66x} +20 \\\Leftrightarrow & 550x \color{red}{-55} \color{blue}{+55} \color{blue}{+66x} & = & \color{red}{-66x} +20 \color{blue}{+66x} \color{blue}{+55} \\\Leftrightarrow & 550x+66x& = & 20+55 \\\Leftrightarrow & \color{red}{616} x& = & 75 \\\Leftrightarrow & x = \frac{75}{616} & & \\ & V = \left\{ \frac{75}{616} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{9}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{-98x} +63 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-18} \\\Leftrightarrow & 168x+98x& = & 63-18 \\\Leftrightarrow & \color{red}{266} x& = & 45 \\\Leftrightarrow & x = \frac{45}{266} & & \\ & V = \left\{ \frac{45}{266} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{11})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x-\frac{30}{11}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3960}{ \color{blue}{132} }x- \frac{360}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3960x \color{red}{-360} & = & \color{red}{-924x} +55 \\\Leftrightarrow & -3960x \color{red}{-360} \color{blue}{+360} \color{blue}{+924x} & = & \color{red}{-924x} +55 \color{blue}{+924x} \color{blue}{+360} \\\Leftrightarrow & -3960x+924x& = & 55+360 \\\Leftrightarrow & \color{red}{-3036} x& = & 415 \\\Leftrightarrow & x = \frac{415}{-3036} & & \\\Leftrightarrow & x = \frac{-415}{3036} & & \\ & V = \left\{ \frac{-415}{3036} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-220} & = & \color{red}{231x} +12 \\\Leftrightarrow & -660x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +12 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & -660x-231x& = & 12+220 \\\Leftrightarrow & \color{red}{-891} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-891} & & \\\Leftrightarrow & x = \frac{-232}{891} & & \\ & V = \left\{ \frac{-232}{891} \right\} & \\\end{align}\)