Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{5})& = & 8x+\frac{5}{11} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1925}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1925x \color{red}{-154} & = & \color{red}{440x} +25 \\\Leftrightarrow & 1925x \color{red}{-154} \color{blue}{+154} \color{blue}{-440x} & = & \color{red}{440x} +25 \color{blue}{-440x} \color{blue}{+154} \\\Leftrightarrow & 1925x-440x& = & 25+154 \\\Leftrightarrow & \color{red}{1485} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1485} & & \\ & V = \left\{ \frac{179}{1485} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{5})& = & 3x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{8}{5}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-16} & = & \color{red}{30x} +3 \\\Leftrightarrow & -200x \color{red}{-16} \color{blue}{+16} \color{blue}{-30x} & = & \color{red}{30x} +3 \color{blue}{-30x} \color{blue}{+16} \\\Leftrightarrow & -200x-30x& = & 3+16 \\\Leftrightarrow & \color{red}{-230} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-230} & & \\\Leftrightarrow & x = \frac{-19}{230} & & \\ & V = \left\{ \frac{-19}{230} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{9})& = & 6x+\frac{8}{11} \\\Leftrightarrow & -35x-\frac{14}{9}& = & 6x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-154} & = & \color{red}{594x} +72 \\\Leftrightarrow & -3465x \color{red}{-154} \color{blue}{+154} \color{blue}{-594x} & = & \color{red}{594x} +72 \color{blue}{-594x} \color{blue}{+154} \\\Leftrightarrow & -3465x-594x& = & 72+154 \\\Leftrightarrow & \color{red}{-4059} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-4059} & & \\\Leftrightarrow & x = \frac{-226}{4059} & & \\ & V = \left\{ \frac{-226}{4059} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{7}{12} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{112}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-112} & = & \color{red}{-96x} +7 \\\Leftrightarrow & -252x \color{red}{-112} \color{blue}{+112} \color{blue}{+96x} & = & \color{red}{-96x} +7 \color{blue}{+96x} \color{blue}{+112} \\\Leftrightarrow & -252x+96x& = & 7+112 \\\Leftrightarrow & \color{red}{-156} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-156} & & \\\Leftrightarrow & x = \frac{-119}{156} & & \\ & V = \left\{ \frac{-119}{156} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{12})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -28x+\frac{35}{12}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{70}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+70} & = & \color{red}{-216x} +21 \\\Leftrightarrow & -672x \color{red}{+70} \color{blue}{-70} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{-70} \\\Leftrightarrow & -672x+216x& = & 21-70 \\\Leftrightarrow & \color{red}{-456} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-456} & & \\\Leftrightarrow & x = \frac{49}{456} & & \\ & V = \left\{ \frac{49}{456} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{175x} +25 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & 210x-175x& = & 25+42 \\\Leftrightarrow & \color{red}{35} x& = & 67 \\\Leftrightarrow & x = \frac{67}{35} & & \\ & V = \left\{ \frac{67}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+8} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{-8} \\\Leftrightarrow & -24x+9x& = & 4-8 \\\Leftrightarrow & \color{red}{-15} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-15} & & \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -3x+\frac{7}{3} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+18} & = & \color{red}{-63x} +49 \\\Leftrightarrow & -168x \color{red}{+18} \color{blue}{-18} \color{blue}{+63x} & = & \color{red}{-63x} +49 \color{blue}{+63x} \color{blue}{-18} \\\Leftrightarrow & -168x+63x& = & 49-18 \\\Leftrightarrow & \color{red}{-105} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-105} & & \\\Leftrightarrow & x = \frac{-31}{105} & & \\ & V = \left\{ \frac{-31}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{7})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{20}{7}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-220} & = & \color{red}{308x} +42 \\\Leftrightarrow & -1155x \color{red}{-220} \color{blue}{+220} \color{blue}{-308x} & = & \color{red}{308x} +42 \color{blue}{-308x} \color{blue}{+220} \\\Leftrightarrow & -1155x-308x& = & 42+220 \\\Leftrightarrow & \color{red}{-1463} x& = & 262 \\\Leftrightarrow & x = \frac{262}{-1463} & & \\\Leftrightarrow & x = \frac{-262}{1463} & & \\ & V = \left\{ \frac{-262}{1463} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{231x} +22 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & -330x-231x& = & 22-30 \\\Leftrightarrow & \color{red}{-561} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-561} & & \\\Leftrightarrow & x = \frac{8}{561} & & \\ & V = \left\{ \frac{8}{561} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 60x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{35} x& = & 18 \\\Leftrightarrow & x = \frac{18}{35} & & \\ & V = \left\{ \frac{18}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{2})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{21}{2}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{-105} & = & \color{red}{30x} +12 \\\Leftrightarrow & 280x \color{red}{-105} \color{blue}{+105} \color{blue}{-30x} & = & \color{red}{30x} +12 \color{blue}{-30x} \color{blue}{+105} \\\Leftrightarrow & 280x-30x& = & 12+105 \\\Leftrightarrow & \color{red}{250} x& = & 117 \\\Leftrightarrow & x = \frac{117}{250} & & \\ & V = \left\{ \frac{117}{250} \right\} & \\\end{align}\)