Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{+12} & = & \color{red}{35x} +4 \\\Leftrightarrow & 100x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 100x-35x& = & 4-12 \\\Leftrightarrow & \color{red}{65} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{65} & & \\ & V = \left\{ \frac{-8}{65} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{10}{11}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+20} & = & \color{red}{44x} +33 \\\Leftrightarrow & 330x \color{red}{+20} \color{blue}{-20} \color{blue}{-44x} & = & \color{red}{44x} +33 \color{blue}{-44x} \color{blue}{-20} \\\Leftrightarrow & 330x-44x& = & 33-20 \\\Leftrightarrow & \color{red}{286} x& = & 13 \\\Leftrightarrow & x = \frac{13}{286} & & \\\Leftrightarrow & x = \frac{1}{22} & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{11})& = & -9x+\frac{5}{9} \\\Leftrightarrow & 4x-\frac{10}{11}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-90} & = & \color{red}{-891x} +55 \\\Leftrightarrow & 396x \color{red}{-90} \color{blue}{+90} \color{blue}{+891x} & = & \color{red}{-891x} +55 \color{blue}{+891x} \color{blue}{+90} \\\Leftrightarrow & 396x+891x& = & 55+90 \\\Leftrightarrow & \color{red}{1287} x& = & 145 \\\Leftrightarrow & x = \frac{145}{1287} & & \\ & V = \left\{ \frac{145}{1287} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{-60} & = & \color{red}{-210x} +49 \\\Leftrightarrow & -560x \color{red}{-60} \color{blue}{+60} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+60} \\\Leftrightarrow & -560x+210x& = & 49+60 \\\Leftrightarrow & \color{red}{-350} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-350} & & \\\Leftrightarrow & x = \frac{-109}{350} & & \\ & V = \left\{ \frac{-109}{350} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 10x+\frac{8}{7}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+64} & = & \color{red}{-504x} +35 \\\Leftrightarrow & 560x \color{red}{+64} \color{blue}{-64} \color{blue}{+504x} & = & \color{red}{-504x} +35 \color{blue}{+504x} \color{blue}{-64} \\\Leftrightarrow & 560x+504x& = & 35-64 \\\Leftrightarrow & \color{red}{1064} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{1064} & & \\ & V = \left\{ \frac{-29}{1064} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{6})& = & -6x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{25}{6}& = & -6x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+25} & = & \color{red}{-36x} +4 \\\Leftrightarrow & 150x \color{red}{+25} \color{blue}{-25} \color{blue}{+36x} & = & \color{red}{-36x} +4 \color{blue}{+36x} \color{blue}{-25} \\\Leftrightarrow & 150x+36x& = & 4-25 \\\Leftrightarrow & \color{red}{186} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{186} & & \\\Leftrightarrow & x = \frac{-7}{62} & & \\ & V = \left\{ \frac{-7}{62} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -6x+\frac{9}{5}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+81} & = & \color{red}{315x} +35 \\\Leftrightarrow & -270x \color{red}{+81} \color{blue}{-81} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-81} \\\Leftrightarrow & -270x-315x& = & 35-81 \\\Leftrightarrow & \color{red}{-585} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-585} & & \\\Leftrightarrow & x = \frac{46}{585} & & \\ & V = \left\{ \frac{46}{585} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{72}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+72} & = & \color{red}{-140x} +45 \\\Leftrightarrow & 480x \color{red}{+72} \color{blue}{-72} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{-72} \\\Leftrightarrow & 480x+140x& = & 45-72 \\\Leftrightarrow & \color{red}{620} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{620} & & \\ & V = \left\{ \frac{-27}{620} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{6})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-125} & = & \color{red}{210x} +36 \\\Leftrightarrow & 300x \color{red}{-125} \color{blue}{+125} \color{blue}{-210x} & = & \color{red}{210x} +36 \color{blue}{-210x} \color{blue}{+125} \\\Leftrightarrow & 300x-210x& = & 36+125 \\\Leftrightarrow & \color{red}{90} x& = & 161 \\\Leftrightarrow & x = \frac{161}{90} & & \\ & V = \left\{ \frac{161}{90} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -4x+\frac{10}{9}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+70} & = & \color{red}{315x} +90 \\\Leftrightarrow & -252x \color{red}{+70} \color{blue}{-70} \color{blue}{-315x} & = & \color{red}{315x} +90 \color{blue}{-315x} \color{blue}{-70} \\\Leftrightarrow & -252x-315x& = & 90-70 \\\Leftrightarrow & \color{red}{-567} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-567} & & \\\Leftrightarrow & x = \frac{-20}{567} & & \\ & V = \left\{ \frac{-20}{567} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -90x+35x& = & 8-12 \\\Leftrightarrow & \color{red}{-55} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-55} & & \\\Leftrightarrow & x = \frac{4}{55} & & \\ & V = \left\{ \frac{4}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{9})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-16} & = & \color{red}{-162x} +45 \\\Leftrightarrow & -144x \color{red}{-16} \color{blue}{+16} \color{blue}{+162x} & = & \color{red}{-162x} +45 \color{blue}{+162x} \color{blue}{+16} \\\Leftrightarrow & -144x+162x& = & 45+16 \\\Leftrightarrow & \color{red}{18} x& = & 61 \\\Leftrightarrow & x = \frac{61}{18} & & \\ & V = \left\{ \frac{61}{18} \right\} & \\\end{align}\)