Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-45x} +20 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+45x} & = & \color{red}{-45x} +20 \color{blue}{+45x} \color{blue}{-12} \\\Leftrightarrow & 60x+45x& = & 20-12 \\\Leftrightarrow & \color{red}{105} x& = & 8 \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{8})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{-200x} +48 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{+200x} & = & \color{red}{-200x} +48 \color{blue}{+200x} \color{blue}{-75} \\\Leftrightarrow & 480x+200x& = & 48-75 \\\Leftrightarrow & \color{red}{680} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{680} & & \\ & V = \left\{ \frac{-27}{680} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{2})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 21x-\frac{21}{2}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{6}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{-231} & = & \color{red}{44x} +6 \\\Leftrightarrow & 462x \color{red}{-231} \color{blue}{+231} \color{blue}{-44x} & = & \color{red}{44x} +6 \color{blue}{-44x} \color{blue}{+231} \\\Leftrightarrow & 462x-44x& = & 6+231 \\\Leftrightarrow & \color{red}{418} x& = & 237 \\\Leftrightarrow & x = \frac{237}{418} & & \\ & V = \left\{ \frac{237}{418} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+150} & = & \color{red}{245x} +14 \\\Leftrightarrow & 1050x \color{red}{+150} \color{blue}{-150} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-150} \\\Leftrightarrow & 1050x-245x& = & 14-150 \\\Leftrightarrow & \color{red}{805} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{805} & & \\ & V = \left\{ \frac{-136}{805} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-270} & = & \color{red}{-315x} +70 \\\Leftrightarrow & -756x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -756x+315x& = & 70+270 \\\Leftrightarrow & \color{red}{-441} x& = & 340 \\\Leftrightarrow & x = \frac{340}{-441} & & \\\Leftrightarrow & x = \frac{-340}{441} & & \\ & V = \left\{ \frac{-340}{441} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{-40} & = & \color{red}{-30x} +7 \\\Leftrightarrow & -72x \color{red}{-40} \color{blue}{+40} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{+40} \\\Leftrightarrow & -72x+30x& = & 7+40 \\\Leftrightarrow & \color{red}{-42} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-42} & & \\\Leftrightarrow & x = \frac{-47}{42} & & \\ & V = \left\{ \frac{-47}{42} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{10}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{-20} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 176x \color{red}{-20} \color{blue}{+20} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+20} \\\Leftrightarrow & 176x+110x& = & 99+20 \\\Leftrightarrow & \color{red}{286} x& = & 119 \\\Leftrightarrow & x = \frac{119}{286} & & \\ & V = \left\{ \frac{119}{286} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{9}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-9} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -63x \color{red}{-9} \color{blue}{+9} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+9} \\\Leftrightarrow & -63x+49x& = & 4+9 \\\Leftrightarrow & \color{red}{-14} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-14} & & \\\Leftrightarrow & x = \frac{-13}{14} & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-55x} +4 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & -264x+55x& = & 4-18 \\\Leftrightarrow & \color{red}{-209} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-209} & & \\\Leftrightarrow & x = \frac{14}{209} & & \\ & V = \left\{ \frac{14}{209} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{10}{11}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+70} & = & \color{red}{693x} +110 \\\Leftrightarrow & 1540x \color{red}{+70} \color{blue}{-70} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-70} \\\Leftrightarrow & 1540x-693x& = & 110-70 \\\Leftrightarrow & \color{red}{847} x& = & 40 \\\Leftrightarrow & x = \frac{40}{847} & & \\ & V = \left\{ \frac{40}{847} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+112} & = & \color{red}{192x} +27 \\\Leftrightarrow & -504x \color{red}{+112} \color{blue}{-112} \color{blue}{-192x} & = & \color{red}{192x} +27 \color{blue}{-192x} \color{blue}{-112} \\\Leftrightarrow & -504x-192x& = & 27-112 \\\Leftrightarrow & \color{red}{-696} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-696} & & \\\Leftrightarrow & x = \frac{85}{696} & & \\ & V = \left\{ \frac{85}{696} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-50} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -550x \color{red}{-50} \color{blue}{+50} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+50} \\\Leftrightarrow & -550x+385x& = & 66+50 \\\Leftrightarrow & \color{red}{-165} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-165} & & \\\Leftrightarrow & x = \frac{-116}{165} & & \\ & V = \left\{ \frac{-116}{165} \right\} & \\\end{align}\)