Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-210} & = & \color{red}{385x} +22 \\\Leftrightarrow & -924x \color{red}{-210} \color{blue}{+210} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+210} \\\Leftrightarrow & -924x-385x& = & 22+210 \\\Leftrightarrow & \color{red}{-1309} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-1309} & & \\\Leftrightarrow & x = \frac{-232}{1309} & & \\ & V = \left\{ \frac{-232}{1309} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{2})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 28x-\frac{35}{2}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x- \frac{175}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{-175} & = & \color{red}{90x} +3 \\\Leftrightarrow & 280x \color{red}{-175} \color{blue}{+175} \color{blue}{-90x} & = & \color{red}{90x} +3 \color{blue}{-90x} \color{blue}{+175} \\\Leftrightarrow & 280x-90x& = & 3+175 \\\Leftrightarrow & \color{red}{190} x& = & 178 \\\Leftrightarrow & x = \frac{178}{190} & & \\\Leftrightarrow & x = \frac{89}{95} & & \\ & V = \left\{ \frac{89}{95} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{-189x} +30 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{-140} \\\Leftrightarrow & -168x+189x& = & 30-140 \\\Leftrightarrow & \color{red}{21} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{21} & & \\ & V = \left\{ \frac{-110}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+100} & = & \color{red}{315x} +28 \\\Leftrightarrow & 700x \color{red}{+100} \color{blue}{-100} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-100} \\\Leftrightarrow & 700x-315x& = & 28-100 \\\Leftrightarrow & \color{red}{385} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{385} & & \\ & V = \left\{ \frac{-72}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+72} & = & \color{red}{308x} +33 \\\Leftrightarrow & 1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & 1320x-308x& = & 33-72 \\\Leftrightarrow & \color{red}{1012} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{1012} & & \\ & V = \left\{ \frac{-39}{1012} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & -4x+\frac{5}{3} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+36} & = & \color{red}{-60x} +25 \\\Leftrightarrow & -225x \color{red}{+36} \color{blue}{-36} \color{blue}{+60x} & = & \color{red}{-60x} +25 \color{blue}{+60x} \color{blue}{-36} \\\Leftrightarrow & -225x+60x& = & 25-36 \\\Leftrightarrow & \color{red}{-165} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-165} & & \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{7})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{15}{7}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{-45} & = & \color{red}{42x} +28 \\\Leftrightarrow & 189x \color{red}{-45} \color{blue}{+45} \color{blue}{-42x} & = & \color{red}{42x} +28 \color{blue}{-42x} \color{blue}{+45} \\\Leftrightarrow & 189x-42x& = & 28+45 \\\Leftrightarrow & \color{red}{147} x& = & 73 \\\Leftrightarrow & x = \frac{73}{147} & & \\ & V = \left\{ \frac{73}{147} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-42} & = & \color{red}{-66x} +99 \\\Leftrightarrow & -308x \color{red}{-42} \color{blue}{+42} \color{blue}{+66x} & = & \color{red}{-66x} +99 \color{blue}{+66x} \color{blue}{+42} \\\Leftrightarrow & -308x+66x& = & 99+42 \\\Leftrightarrow & \color{red}{-242} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-242} & & \\\Leftrightarrow & x = \frac{-141}{242} & & \\ & V = \left\{ \frac{-141}{242} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{9})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 16x-\frac{20}{9}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-100} & = & \color{red}{-225x} +81 \\\Leftrightarrow & 720x \color{red}{-100} \color{blue}{+100} \color{blue}{+225x} & = & \color{red}{-225x} +81 \color{blue}{+225x} \color{blue}{+100} \\\Leftrightarrow & 720x+225x& = & 81+100 \\\Leftrightarrow & \color{red}{945} x& = & 181 \\\Leftrightarrow & x = \frac{181}{945} & & \\ & V = \left\{ \frac{181}{945} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{15}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+75} & = & \color{red}{315x} +42 \\\Leftrightarrow & 350x \color{red}{+75} \color{blue}{-75} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{-75} \\\Leftrightarrow & 350x-315x& = & 42-75 \\\Leftrightarrow & \color{red}{35} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{35} & & \\ & V = \left\{ \frac{-33}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+150} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & 420x+175x& = & 28-150 \\\Leftrightarrow & \color{red}{595} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{595} & & \\ & V = \left\{ \frac{-122}{595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-8} & = & \color{red}{27x} +12 \\\Leftrightarrow & 180x \color{red}{-8} \color{blue}{+8} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{+8} \\\Leftrightarrow & 180x-27x& = & 12+8 \\\Leftrightarrow & \color{red}{153} x& = & 20 \\\Leftrightarrow & x = \frac{20}{153} & & \\ & V = \left\{ \frac{20}{153} \right\} & \\\end{align}\)