Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{15}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-45} & = & \color{red}{165x} +110 \\\Leftrightarrow & 198x \color{red}{-45} \color{blue}{+45} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+45} \\\Leftrightarrow & 198x-165x& = & 110+45 \\\Leftrightarrow & \color{red}{33} x& = & 155 \\\Leftrightarrow & x = \frac{155}{33} & & \\ & V = \left\{ \frac{155}{33} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-30} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 126x-105x& = & 70+30 \\\Leftrightarrow & \color{red}{21} x& = & 100 \\\Leftrightarrow & x = \frac{100}{21} & & \\ & V = \left\{ \frac{100}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+60} & = & \color{red}{-81x} +2 \\\Leftrightarrow & -72x \color{red}{+60} \color{blue}{-60} \color{blue}{+81x} & = & \color{red}{-81x} +2 \color{blue}{+81x} \color{blue}{-60} \\\Leftrightarrow & -72x+81x& = & 2-60 \\\Leftrightarrow & \color{red}{9} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{9} & & \\ & V = \left\{ \frac{-58}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{8})& = & -9x+\frac{5}{12} \\\Leftrightarrow & 25x+\frac{25}{8}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x+ \frac{75}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{+75} & = & \color{red}{-216x} +10 \\\Leftrightarrow & 600x \color{red}{+75} \color{blue}{-75} \color{blue}{+216x} & = & \color{red}{-216x} +10 \color{blue}{+216x} \color{blue}{-75} \\\Leftrightarrow & 600x+216x& = & 10-75 \\\Leftrightarrow & \color{red}{816} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{816} & & \\ & V = \left\{ \frac{-65}{816} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{-72} & = & \color{red}{-210x} +35 \\\Leftrightarrow & -480x \color{red}{-72} \color{blue}{+72} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{+72} \\\Leftrightarrow & -480x+210x& = & 35+72 \\\Leftrightarrow & \color{red}{-270} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-270} & & \\\Leftrightarrow & x = \frac{-107}{270} & & \\ & V = \left\{ \frac{-107}{270} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-84} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -630x \color{red}{-84} \color{blue}{+84} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+84} \\\Leftrightarrow & -630x+315x& = & 20+84 \\\Leftrightarrow & \color{red}{-315} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-315} & & \\\Leftrightarrow & x = \frac{-104}{315} & & \\ & V = \left\{ \frac{-104}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{5})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 4x+\frac{8}{5}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{+16} & = & \color{red}{-90x} +35 \\\Leftrightarrow & 40x \color{red}{+16} \color{blue}{-16} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{-16} \\\Leftrightarrow & 40x+90x& = & 35-16 \\\Leftrightarrow & \color{red}{130} x& = & 19 \\\Leftrightarrow & x = \frac{19}{130} & & \\ & V = \left\{ \frac{19}{130} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{4})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{4}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{+125} & = & \color{red}{60x} +24 \\\Leftrightarrow & 200x \color{red}{+125} \color{blue}{-125} \color{blue}{-60x} & = & \color{red}{60x} +24 \color{blue}{-60x} \color{blue}{-125} \\\Leftrightarrow & 200x-60x& = & 24-125 \\\Leftrightarrow & \color{red}{140} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{140} & & \\ & V = \left\{ \frac{-101}{140} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{3})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 10x+\frac{25}{3}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{100}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+100} & = & \color{red}{-36x} +5 \\\Leftrightarrow & 120x \color{red}{+100} \color{blue}{-100} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{-100} \\\Leftrightarrow & 120x+36x& = & 5-100 \\\Leftrightarrow & \color{red}{156} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{156} & & \\ & V = \left\{ \frac{-95}{156} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{11})& = & -8x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{28}{11}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1617}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1617x \color{red}{-196} & = & \color{red}{-616x} +99 \\\Leftrightarrow & 1617x \color{red}{-196} \color{blue}{+196} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{+196} \\\Leftrightarrow & 1617x+616x& = & 99+196 \\\Leftrightarrow & \color{red}{2233} x& = & 295 \\\Leftrightarrow & x = \frac{295}{2233} & & \\ & V = \left\{ \frac{295}{2233} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{9})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -28x+\frac{28}{9}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{+196} & = & \color{red}{567x} +81 \\\Leftrightarrow & -1764x \color{red}{+196} \color{blue}{-196} \color{blue}{-567x} & = & \color{red}{567x} +81 \color{blue}{-567x} \color{blue}{-196} \\\Leftrightarrow & -1764x-567x& = & 81-196 \\\Leftrightarrow & \color{red}{-2331} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{-2331} & & \\\Leftrightarrow & x = \frac{115}{2331} & & \\ & V = \left\{ \frac{115}{2331} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{315x} +28 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & -1512x-315x& = & 28+270 \\\Leftrightarrow & \color{red}{-1827} x& = & 298 \\\Leftrightarrow & x = \frac{298}{-1827} & & \\\Leftrightarrow & x = \frac{-298}{1827} & & \\ & V = \left\{ \frac{-298}{1827} \right\} & \\\end{align}\)