Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & 5x+\frac{5}{3} \\\Leftrightarrow & -4x-\frac{10}{11}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{165x} +55 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{-165x} & = & \color{red}{165x} +55 \color{blue}{-165x} \color{blue}{+30} \\\Leftrightarrow & -132x-165x& = & 55+30 \\\Leftrightarrow & \color{red}{-297} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-297} & & \\\Leftrightarrow & x = \frac{-85}{297} & & \\ & V = \left\{ \frac{-85}{297} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{+36} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 660x \color{red}{+36} \color{blue}{-36} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-36} \\\Leftrightarrow & 660x+154x& = & 33-36 \\\Leftrightarrow & \color{red}{814} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{814} & & \\ & V = \left\{ \frac{-3}{814} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{8}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+8} & = & \color{red}{21x} +4 \\\Leftrightarrow & -30x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -30x-21x& = & 4-8 \\\Leftrightarrow & \color{red}{-51} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-51} & & \\\Leftrightarrow & x = \frac{4}{51} & & \\ & V = \left\{ \frac{4}{51} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-44} & = & \color{red}{-385x} +20 \\\Leftrightarrow & 220x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & 220x+385x& = & 20+44 \\\Leftrightarrow & \color{red}{605} x& = & 64 \\\Leftrightarrow & x = \frac{64}{605} & & \\ & V = \left\{ \frac{64}{605} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{10}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{-20} & = & \color{red}{-54x} +9 \\\Leftrightarrow & -48x \color{red}{-20} \color{blue}{+20} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{+20} \\\Leftrightarrow & -48x+54x& = & 9+20 \\\Leftrightarrow & \color{red}{6} x& = & 29 \\\Leftrightarrow & x = \frac{29}{6} & & \\ & V = \left\{ \frac{29}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{14}{11}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{70}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-70} & = & \color{red}{220x} +66 \\\Leftrightarrow & -1925x \color{red}{-70} \color{blue}{+70} \color{blue}{-220x} & = & \color{red}{220x} +66 \color{blue}{-220x} \color{blue}{+70} \\\Leftrightarrow & -1925x-220x& = & 66+70 \\\Leftrightarrow & \color{red}{-2145} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-2145} & & \\\Leftrightarrow & x = \frac{-136}{2145} & & \\ & V = \left\{ \frac{-136}{2145} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & 2x+\frac{5}{3} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 2x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-45} & = & \color{red}{48x} +40 \\\Leftrightarrow & 360x \color{red}{-45} \color{blue}{+45} \color{blue}{-48x} & = & \color{red}{48x} +40 \color{blue}{-48x} \color{blue}{+45} \\\Leftrightarrow & 360x-48x& = & 40+45 \\\Leftrightarrow & \color{red}{312} x& = & 85 \\\Leftrightarrow & x = \frac{85}{312} & & \\ & V = \left\{ \frac{85}{312} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-220} & = & \color{red}{-231x} +6 \\\Leftrightarrow & 495x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +6 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 495x+231x& = & 6+220 \\\Leftrightarrow & \color{red}{726} x& = & 226 \\\Leftrightarrow & x = \frac{226}{726} & & \\\Leftrightarrow & x = \frac{113}{363} & & \\ & V = \left\{ \frac{113}{363} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -3x+\frac{7}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -3x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{-189x} +49 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{+189x} & = & \color{red}{-189x} +49 \color{blue}{+189x} \color{blue}{+54} \\\Leftrightarrow & 504x+189x& = & 49+54 \\\Leftrightarrow & \color{red}{693} x& = & 103 \\\Leftrightarrow & x = \frac{103}{693} & & \\ & V = \left\{ \frac{103}{693} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{385x} +10 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 660x-385x& = & 10+132 \\\Leftrightarrow & \color{red}{275} x& = & 142 \\\Leftrightarrow & x = \frac{142}{275} & & \\ & V = \left\{ \frac{142}{275} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+96} & = & \color{red}{308x} +77 \\\Leftrightarrow & 1320x \color{red}{+96} \color{blue}{-96} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{-96} \\\Leftrightarrow & 1320x-308x& = & 77-96 \\\Leftrightarrow & \color{red}{1012} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{1012} & & \\ & V = \left\{ \frac{-19}{1012} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{12}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+84} & = & \color{red}{539x} +110 \\\Leftrightarrow & 1848x \color{red}{+84} \color{blue}{-84} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-84} \\\Leftrightarrow & 1848x-539x& = & 110-84 \\\Leftrightarrow & \color{red}{1309} x& = & 26 \\\Leftrightarrow & x = \frac{26}{1309} & & \\ & V = \left\{ \frac{26}{1309} \right\} & \\\end{align}\)