Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 270x-75x& = & 20+36 \\\Leftrightarrow & \color{red}{195} x& = & 56 \\\Leftrightarrow & x = \frac{56}{195} & & \\ & V = \left\{ \frac{56}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -30x-\frac{18}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-162} & = & \color{red}{315x} +40 \\\Leftrightarrow & -1350x \color{red}{-162} \color{blue}{+162} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+162} \\\Leftrightarrow & -1350x-315x& = & 40+162 \\\Leftrightarrow & \color{red}{-1665} x& = & 202 \\\Leftrightarrow & x = \frac{202}{-1665} & & \\\Leftrightarrow & x = \frac{-202}{1665} & & \\ & V = \left\{ \frac{-202}{1665} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-245x} +63 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -210x+245x& = & 63-30 \\\Leftrightarrow & \color{red}{35} x& = & 33 \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{14}{9}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-98} & = & \color{red}{315x} +27 \\\Leftrightarrow & 882x \color{red}{-98} \color{blue}{+98} \color{blue}{-315x} & = & \color{red}{315x} +27 \color{blue}{-315x} \color{blue}{+98} \\\Leftrightarrow & 882x-315x& = & 27+98 \\\Leftrightarrow & \color{red}{567} x& = & 125 \\\Leftrightarrow & x = \frac{125}{567} & & \\ & V = \left\{ \frac{125}{567} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{10})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{9}{10}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-9} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 120x \color{red}{-9} \color{blue}{+9} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+9} \\\Leftrightarrow & 120x+70x& = & 45+9 \\\Leftrightarrow & \color{red}{190} x& = & 54 \\\Leftrightarrow & x = \frac{54}{190} & & \\\Leftrightarrow & x = \frac{27}{95} & & \\ & V = \left\{ \frac{27}{95} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-144} & = & \color{red}{441x} +70 \\\Leftrightarrow & 1008x \color{red}{-144} \color{blue}{+144} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{+144} \\\Leftrightarrow & 1008x-441x& = & 70+144 \\\Leftrightarrow & \color{red}{567} x& = & 214 \\\Leftrightarrow & x = \frac{214}{567} & & \\ & V = \left\{ \frac{214}{567} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{5})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -20x-\frac{16}{5}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{64}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-64} & = & \color{red}{140x} +25 \\\Leftrightarrow & -400x \color{red}{-64} \color{blue}{+64} \color{blue}{-140x} & = & \color{red}{140x} +25 \color{blue}{-140x} \color{blue}{+64} \\\Leftrightarrow & -400x-140x& = & 25+64 \\\Leftrightarrow & \color{red}{-540} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-540} & & \\\Leftrightarrow & x = \frac{-89}{540} & & \\ & V = \left\{ \frac{-89}{540} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{12}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x+ \frac{120}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{+120} & = & \color{red}{490x} +63 \\\Leftrightarrow & -420x \color{red}{+120} \color{blue}{-120} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-120} \\\Leftrightarrow & -420x-490x& = & 63-120 \\\Leftrightarrow & \color{red}{-910} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-910} & & \\\Leftrightarrow & x = \frac{57}{910} & & \\ & V = \left\{ \frac{57}{910} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{28}{9}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{81x} +24 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{-81x} & = & \color{red}{81x} +24 \color{blue}{-81x} \color{blue}{-28} \\\Leftrightarrow & 126x-81x& = & 24-28 \\\Leftrightarrow & \color{red}{45} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 270x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{345} x& = & 4 \\\Leftrightarrow & x = \frac{4}{345} & & \\ & V = \left\{ \frac{4}{345} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-108} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -720x \color{red}{-108} \color{blue}{+108} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+108} \\\Leftrightarrow & -720x+315x& = & 20+108 \\\Leftrightarrow & \color{red}{-405} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-405} & & \\\Leftrightarrow & x = \frac{-128}{405} & & \\ & V = \left\{ \frac{-128}{405} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{+90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -504x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & -504x+147x& = & 70-90 \\\Leftrightarrow & \color{red}{-357} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-357} & & \\\Leftrightarrow & x = \frac{20}{357} & & \\ & V = \left\{ \frac{20}{357} \right\} & \\\end{align}\)