Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{+147} & = & \color{red}{168x} +64 \\\Leftrightarrow & -784x \color{red}{+147} \color{blue}{-147} \color{blue}{-168x} & = & \color{red}{168x} +64 \color{blue}{-168x} \color{blue}{-147} \\\Leftrightarrow & -784x-168x& = & 64-147 \\\Leftrightarrow & \color{red}{-952} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-952} & & \\\Leftrightarrow & x = \frac{83}{952} & & \\ & V = \left\{ \frac{83}{952} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2310}{ \color{blue}{110} }x- \frac{210}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2310x \color{red}{-210} & = & \color{red}{-550x} +77 \\\Leftrightarrow & 2310x \color{red}{-210} \color{blue}{+210} \color{blue}{+550x} & = & \color{red}{-550x} +77 \color{blue}{+550x} \color{blue}{+210} \\\Leftrightarrow & 2310x+550x& = & 77+210 \\\Leftrightarrow & \color{red}{2860} x& = & 287 \\\Leftrightarrow & x = \frac{287}{2860} & & \\ & V = \left\{ \frac{287}{2860} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{5})& = & -2x+\frac{7}{10} \\\Leftrightarrow & 35x+\frac{28}{5}& = & -2x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{56}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+56} & = & \color{red}{-20x} +7 \\\Leftrightarrow & 350x \color{red}{+56} \color{blue}{-56} \color{blue}{+20x} & = & \color{red}{-20x} +7 \color{blue}{+20x} \color{blue}{-56} \\\Leftrightarrow & 350x+20x& = & 7-56 \\\Leftrightarrow & \color{red}{370} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{370} & & \\ & V = \left\{ \frac{-49}{370} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{196x} +49 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{+40} \\\Leftrightarrow & 280x-196x& = & 49+40 \\\Leftrightarrow & \color{red}{84} x& = & 89 \\\Leftrightarrow & x = \frac{89}{84} & & \\ & V = \left\{ \frac{89}{84} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{9})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 20x+\frac{16}{9}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{176}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+176} & = & \color{red}{297x} +27 \\\Leftrightarrow & 1980x \color{red}{+176} \color{blue}{-176} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{-176} \\\Leftrightarrow & 1980x-297x& = & 27-176 \\\Leftrightarrow & \color{red}{1683} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{1683} & & \\ & V = \left\{ \frac{-149}{1683} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 360x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 360x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{435} x& = & 4 \\\Leftrightarrow & x = \frac{4}{435} & & \\ & V = \left\{ \frac{4}{435} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{-54} & = & \color{red}{441x} +35 \\\Leftrightarrow & 567x \color{red}{-54} \color{blue}{+54} \color{blue}{-441x} & = & \color{red}{441x} +35 \color{blue}{-441x} \color{blue}{+54} \\\Leftrightarrow & 567x-441x& = & 35+54 \\\Leftrightarrow & \color{red}{126} x& = & 89 \\\Leftrightarrow & x = \frac{89}{126} & & \\ & V = \left\{ \frac{89}{126} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{11})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -25x-\frac{10}{11}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{-70} & = & \color{red}{231x} +33 \\\Leftrightarrow & -1925x \color{red}{-70} \color{blue}{+70} \color{blue}{-231x} & = & \color{red}{231x} +33 \color{blue}{-231x} \color{blue}{+70} \\\Leftrightarrow & -1925x-231x& = & 33+70 \\\Leftrightarrow & \color{red}{-2156} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-2156} & & \\\Leftrightarrow & x = \frac{-103}{2156} & & \\ & V = \left\{ \frac{-103}{2156} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{9})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1800}{ \color{blue}{90} }x+ \frac{200}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1800x \color{red}{+200} & = & \color{red}{270x} +27 \\\Leftrightarrow & 1800x \color{red}{+200} \color{blue}{-200} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{-200} \\\Leftrightarrow & 1800x-270x& = & 27-200 \\\Leftrightarrow & \color{red}{1530} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{1530} & & \\ & V = \left\{ \frac{-173}{1530} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & 45x+21x& = & 10+20 \\\Leftrightarrow & \color{red}{66} x& = & 30 \\\Leftrightarrow & x = \frac{30}{66} & & \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{11})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{8}{11}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-24} \\\Leftrightarrow & -132x+297x& = & 88-24 \\\Leftrightarrow & \color{red}{165} x& = & 64 \\\Leftrightarrow & x = \frac{64}{165} & & \\ & V = \left\{ \frac{64}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+63} & = & \color{red}{-245x} +20 \\\Leftrightarrow & 315x \color{red}{+63} \color{blue}{-63} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{-63} \\\Leftrightarrow & 315x+245x& = & 20-63 \\\Leftrightarrow & \color{red}{560} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{560} & & \\ & V = \left\{ \frac{-43}{560} \right\} & \\\end{align}\)