Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-50} & = & \color{red}{-70x} +42 \\\Leftrightarrow & 525x \color{red}{-50} \color{blue}{+50} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{+50} \\\Leftrightarrow & 525x+70x& = & 42+50 \\\Leftrightarrow & \color{red}{595} x& = & 92 \\\Leftrightarrow & x = \frac{92}{595} & & \\ & V = \left\{ \frac{92}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 35x-\frac{35}{9}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{2205}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 2205x \color{red}{-245} & = & \color{red}{189x} +27 \\\Leftrightarrow & 2205x \color{red}{-245} \color{blue}{+245} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{+245} \\\Leftrightarrow & 2205x-189x& = & 27+245 \\\Leftrightarrow & \color{red}{2016} x& = & 272 \\\Leftrightarrow & x = \frac{272}{2016} & & \\\Leftrightarrow & x = \frac{17}{126} & & \\ & V = \left\{ \frac{17}{126} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{7})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 9x+\frac{9}{7}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+9} & = & \color{red}{-14x} +9 \\\Leftrightarrow & 63x \color{red}{+9} \color{blue}{-9} \color{blue}{+14x} & = & \color{red}{-14x} +9 \color{blue}{+14x} \color{blue}{-9} \\\Leftrightarrow & 63x+14x& = & 9-9 \\\Leftrightarrow & \color{red}{77} x& = & 0 \\\Leftrightarrow & x = \frac{0}{77} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{7})& = & 4x+\frac{9}{10} \\\Leftrightarrow & -35x-4& = & 4x+\frac{9}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-350}{ \color{blue}{10} }x- \frac{40}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -350x \color{red}{-40} & = & \color{red}{40x} +9 \\\Leftrightarrow & -350x \color{red}{-40} \color{blue}{+40} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{+40} \\\Leftrightarrow & -350x-40x& = & 9+40 \\\Leftrightarrow & \color{red}{-390} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-390} & & \\\Leftrightarrow & x = \frac{-49}{390} & & \\ & V = \left\{ \frac{-49}{390} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{9})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{25}{9}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{275}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+275} & = & \color{red}{-891x} +36 \\\Leftrightarrow & 1980x \color{red}{+275} \color{blue}{-275} \color{blue}{+891x} & = & \color{red}{-891x} +36 \color{blue}{+891x} \color{blue}{-275} \\\Leftrightarrow & 1980x+891x& = & 36-275 \\\Leftrightarrow & \color{red}{2871} x& = & -239 \\\Leftrightarrow & x = \frac{-239}{2871} & & \\ & V = \left\{ \frac{-239}{2871} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-264} & = & \color{red}{-385x} +10 \\\Leftrightarrow & -990x \color{red}{-264} \color{blue}{+264} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+264} \\\Leftrightarrow & -990x+385x& = & 10+264 \\\Leftrightarrow & \color{red}{-605} x& = & 274 \\\Leftrightarrow & x = \frac{274}{-605} & & \\\Leftrightarrow & x = \frac{-274}{605} & & \\ & V = \left\{ \frac{-274}{605} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{+54} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -567x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & -567x+441x& = & 14-54 \\\Leftrightarrow & \color{red}{-126} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-126} & & \\\Leftrightarrow & x = \frac{20}{63} & & \\ & V = \left\{ \frac{20}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-88} & = & \color{red}{231x} +18 \\\Leftrightarrow & -330x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & -330x-231x& = & 18+88 \\\Leftrightarrow & \color{red}{-561} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-561} & & \\\Leftrightarrow & x = \frac{-106}{561} & & \\ & V = \left\{ \frac{-106}{561} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+270} & = & \color{red}{-315x} +35 \\\Leftrightarrow & 756x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +35 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & 756x+315x& = & 35-270 \\\Leftrightarrow & \color{red}{1071} x& = & -235 \\\Leftrightarrow & x = \frac{-235}{1071} & & \\ & V = \left\{ \frac{-235}{1071} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{7})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{15}{7}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+165} & = & \color{red}{616x} +42 \\\Leftrightarrow & -1155x \color{red}{+165} \color{blue}{-165} \color{blue}{-616x} & = & \color{red}{616x} +42 \color{blue}{-616x} \color{blue}{-165} \\\Leftrightarrow & -1155x-616x& = & 42-165 \\\Leftrightarrow & \color{red}{-1771} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-1771} & & \\\Leftrightarrow & x = \frac{123}{1771} & & \\ & V = \left\{ \frac{123}{1771} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{-693x} +70 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +70 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & 1540x+693x& = & 70-220 \\\Leftrightarrow & \color{red}{2233} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{2233} & & \\ & V = \left\{ \frac{-150}{2233} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-375}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -375x \color{red}{+100} & = & \color{red}{-120x} +18 \\\Leftrightarrow & -375x \color{red}{+100} \color{blue}{-100} \color{blue}{+120x} & = & \color{red}{-120x} +18 \color{blue}{+120x} \color{blue}{-100} \\\Leftrightarrow & -375x+120x& = & 18-100 \\\Leftrightarrow & \color{red}{-255} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-255} & & \\\Leftrightarrow & x = \frac{82}{255} & & \\ & V = \left\{ \frac{82}{255} \right\} & \\\end{align}\)