Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & 6x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{21}{8}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-231} & = & \color{red}{528x} +48 \\\Leftrightarrow & 3080x \color{red}{-231} \color{blue}{+231} \color{blue}{-528x} & = & \color{red}{528x} +48 \color{blue}{-528x} \color{blue}{+231} \\\Leftrightarrow & 3080x-528x& = & 48+231 \\\Leftrightarrow & \color{red}{2552} x& = & 279 \\\Leftrightarrow & x = \frac{279}{2552} & & \\ & V = \left\{ \frac{279}{2552} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-220} & = & \color{red}{-231x} +12 \\\Leftrightarrow & -528x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +12 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -528x+231x& = & 12+220 \\\Leftrightarrow & \color{red}{-297} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-297} & & \\\Leftrightarrow & x = \frac{-232}{297} & & \\ & V = \left\{ \frac{-232}{297} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{49x} +2 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -70x-49x& = & 2-6 \\\Leftrightarrow & \color{red}{-119} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-119} & & \\\Leftrightarrow & x = \frac{4}{119} & & \\ & V = \left\{ \frac{4}{119} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -14x+\frac{14}{9}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-882}{ \color{blue}{63} }x+ \frac{98}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -882x \color{red}{+98} & = & \color{red}{189x} +81 \\\Leftrightarrow & -882x \color{red}{+98} \color{blue}{-98} \color{blue}{-189x} & = & \color{red}{189x} +81 \color{blue}{-189x} \color{blue}{-98} \\\Leftrightarrow & -882x-189x& = & 81-98 \\\Leftrightarrow & \color{red}{-1071} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1071} & & \\\Leftrightarrow & x = \frac{1}{63} & & \\ & V = \left\{ \frac{1}{63} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{11})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{8}{11}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{99x} +44 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{-99x} & = & \color{red}{99x} +44 \color{blue}{-99x} \color{blue}{-24} \\\Leftrightarrow & 132x-99x& = & 44-24 \\\Leftrightarrow & \color{red}{33} x& = & 20 \\\Leftrightarrow & x = \frac{20}{33} & & \\ & V = \left\{ \frac{20}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-10x} +6 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+10x} & = & \color{red}{-10x} +6 \color{blue}{+10x} \color{blue}{-12} \\\Leftrightarrow & 75x+10x& = & 6-12 \\\Leftrightarrow & \color{red}{85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{85} & & \\ & V = \left\{ \frac{-6}{85} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 210x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 210x-175x& = & 10+84 \\\Leftrightarrow & \color{red}{35} x& = & 94 \\\Leftrightarrow & x = \frac{94}{35} & & \\ & V = \left\{ \frac{94}{35} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{8}{9}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+32} & = & \color{red}{-180x} +15 \\\Leftrightarrow & -432x \color{red}{+32} \color{blue}{-32} \color{blue}{+180x} & = & \color{red}{-180x} +15 \color{blue}{+180x} \color{blue}{-32} \\\Leftrightarrow & -432x+180x& = & 15-32 \\\Leftrightarrow & \color{red}{-252} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-252} & & \\\Leftrightarrow & x = \frac{17}{252} & & \\ & V = \left\{ \frac{17}{252} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-42} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -126x \color{red}{-42} \color{blue}{+42} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+42} \\\Leftrightarrow & -126x+27x& = & 4+42 \\\Leftrightarrow & \color{red}{-99} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-99} & & \\\Leftrightarrow & x = \frac{-46}{99} & & \\ & V = \left\{ \frac{-46}{99} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{+24} & = & \color{red}{308x} +99 \\\Leftrightarrow & 440x \color{red}{+24} \color{blue}{-24} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{-24} \\\Leftrightarrow & 440x-308x& = & 99-24 \\\Leftrightarrow & \color{red}{132} x& = & 75 \\\Leftrightarrow & x = \frac{75}{132} & & \\\Leftrightarrow & x = \frac{25}{44} & & \\ & V = \left\{ \frac{25}{44} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{75x} +20 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 180x-75x& = & 20+36 \\\Leftrightarrow & \color{red}{105} x& = & 56 \\\Leftrightarrow & x = \frac{56}{105} & & \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{6}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1584}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1584x \color{red}{+72} & = & \color{red}{660x} +55 \\\Leftrightarrow & 1584x \color{red}{+72} \color{blue}{-72} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{-72} \\\Leftrightarrow & 1584x-660x& = & 55-72 \\\Leftrightarrow & \color{red}{924} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{924} & & \\ & V = \left\{ \frac{-17}{924} \right\} & \\\end{align}\)