Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-66} & = & \color{red}{275x} +20 \\\Leftrightarrow & 330x \color{red}{-66} \color{blue}{+66} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{+66} \\\Leftrightarrow & 330x-275x& = & 20+66 \\\Leftrightarrow & \color{red}{55} x& = & 86 \\\Leftrightarrow & x = \frac{86}{55} & & \\ & V = \left\{ \frac{86}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-175} & = & \color{red}{120x} +18 \\\Leftrightarrow & -315x \color{red}{-175} \color{blue}{+175} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{+175} \\\Leftrightarrow & -315x-120x& = & 18+175 \\\Leftrightarrow & \color{red}{-435} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-435} & & \\\Leftrightarrow & x = \frac{-193}{435} & & \\ & V = \left\{ \frac{-193}{435} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{2})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -28x-\frac{21}{2}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-112}{ \color{blue}{4} }x- \frac{42}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -112x \color{red}{-42} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -112x \color{red}{-42} \color{blue}{+42} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{+42} \\\Leftrightarrow & -112x+20x& = & 9+42 \\\Leftrightarrow & \color{red}{-92} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-92} & & \\\Leftrightarrow & x = \frac{-51}{92} & & \\ & V = \left\{ \frac{-51}{92} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{8})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 10x+\frac{25}{8}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{80}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 80x \color{red}{+25} & = & \color{red}{-56x} +6 \\\Leftrightarrow & 80x \color{red}{+25} \color{blue}{-25} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{-25} \\\Leftrightarrow & 80x+56x& = & 6-25 \\\Leftrightarrow & \color{red}{136} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{136} & & \\ & V = \left\{ \frac{-19}{136} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-300} & = & \color{red}{-490x} +21 \\\Leftrightarrow & 840x \color{red}{-300} \color{blue}{+300} \color{blue}{+490x} & = & \color{red}{-490x} +21 \color{blue}{+490x} \color{blue}{+300} \\\Leftrightarrow & 840x+490x& = & 21+300 \\\Leftrightarrow & \color{red}{1330} x& = & 321 \\\Leftrightarrow & x = \frac{321}{1330} & & \\ & V = \left\{ \frac{321}{1330} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{140x} +21 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{+24} \\\Leftrightarrow & 168x-140x& = & 21+24 \\\Leftrightarrow & \color{red}{28} x& = & 45 \\\Leftrightarrow & x = \frac{45}{28} & & \\ & V = \left\{ \frac{45}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 150x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{115} & & \\ & V = \left\{ \frac{-6}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{9})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{10}{9}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-110} & = & \color{red}{495x} +45 \\\Leftrightarrow & 594x \color{red}{-110} \color{blue}{+110} \color{blue}{-495x} & = & \color{red}{495x} +45 \color{blue}{-495x} \color{blue}{+110} \\\Leftrightarrow & 594x-495x& = & 45+110 \\\Leftrightarrow & \color{red}{99} x& = & 155 \\\Leftrightarrow & x = \frac{155}{99} & & \\ & V = \left\{ \frac{155}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{3})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-220} & = & \color{red}{-231x} +6 \\\Leftrightarrow & -660x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +6 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -660x+231x& = & 6+220 \\\Leftrightarrow & \color{red}{-429} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-429} & & \\\Leftrightarrow & x = \frac{-226}{429} & & \\ & V = \left\{ \frac{-226}{429} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{+36} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -660x \color{red}{+36} \color{blue}{-36} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{-36} \\\Leftrightarrow & -660x+154x& = & 99-36 \\\Leftrightarrow & \color{red}{-506} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-506} & & \\\Leftrightarrow & x = \frac{-63}{506} & & \\ & V = \left\{ \frac{-63}{506} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 8x+\frac{12}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+12} & = & \color{red}{77x} +5 \\\Leftrightarrow & 88x \color{red}{+12} \color{blue}{-12} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{-12} \\\Leftrightarrow & 88x-77x& = & 5-12 \\\Leftrightarrow & \color{red}{11} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-6} & = & \color{red}{35x} +10 \\\Leftrightarrow & 42x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & 42x-35x& = & 10+6 \\\Leftrightarrow & \color{red}{7} x& = & 16 \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)