Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{12}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+108} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -1188x \color{red}{+108} \color{blue}{-108} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-108} \\\Leftrightarrow & -1188x+495x& = & 22-108 \\\Leftrightarrow & \color{red}{-693} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-693} & & \\\Leftrightarrow & x = \frac{86}{693} & & \\ & V = \left\{ \frac{86}{693} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{49x} +2 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{-20} \\\Leftrightarrow & 112x-49x& = & 2-20 \\\Leftrightarrow & \color{red}{63} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{63} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{105x} +42 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 140x-105x& = & 42+30 \\\Leftrightarrow & \color{red}{35} x& = & 72 \\\Leftrightarrow & x = \frac{72}{35} & & \\ & V = \left\{ \frac{72}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+168} & = & \color{red}{245x} +30 \\\Leftrightarrow & 1050x \color{red}{+168} \color{blue}{-168} \color{blue}{-245x} & = & \color{red}{245x} +30 \color{blue}{-245x} \color{blue}{-168} \\\Leftrightarrow & 1050x-245x& = & 30-168 \\\Leftrightarrow & \color{red}{805} x& = & -138 \\\Leftrightarrow & x = \frac{-138}{805} & & \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{8}{9}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{+32} & = & \color{red}{-252x} +27 \\\Leftrightarrow & -360x \color{red}{+32} \color{blue}{-32} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{-32} \\\Leftrightarrow & -360x+252x& = & 27-32 \\\Leftrightarrow & \color{red}{-108} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-108} & & \\\Leftrightarrow & x = \frac{5}{108} & & \\ & V = \left\{ \frac{5}{108} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-96} & = & \color{red}{280x} +45 \\\Leftrightarrow & 1200x \color{red}{-96} \color{blue}{+96} \color{blue}{-280x} & = & \color{red}{280x} +45 \color{blue}{-280x} \color{blue}{+96} \\\Leftrightarrow & 1200x-280x& = & 45+96 \\\Leftrightarrow & \color{red}{920} x& = & 141 \\\Leftrightarrow & x = \frac{141}{920} & & \\ & V = \left\{ \frac{141}{920} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{-66x} +18 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{+66x} & = & \color{red}{-66x} +18 \color{blue}{+66x} \color{blue}{+154} \\\Leftrightarrow & 693x+66x& = & 18+154 \\\Leftrightarrow & \color{red}{759} x& = & 172 \\\Leftrightarrow & x = \frac{172}{759} & & \\ & V = \left\{ \frac{172}{759} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+18} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -252x+105x& = & 56-18 \\\Leftrightarrow & \color{red}{-147} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-147} & & \\\Leftrightarrow & x = \frac{-38}{147} & & \\ & V = \left\{ \frac{-38}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{12})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{25}{12}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{54}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-25} & = & \color{red}{84x} +54 \\\Leftrightarrow & 240x \color{red}{-25} \color{blue}{+25} \color{blue}{-84x} & = & \color{red}{84x} +54 \color{blue}{-84x} \color{blue}{+25} \\\Leftrightarrow & 240x-84x& = & 54+25 \\\Leftrightarrow & \color{red}{156} x& = & 79 \\\Leftrightarrow & x = \frac{79}{156} & & \\ & V = \left\{ \frac{79}{156} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{10})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{-150x} +40 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{+150x} & = & \color{red}{-150x} +40 \color{blue}{+150x} \color{blue}{-27} \\\Leftrightarrow & 180x+150x& = & 40-27 \\\Leftrightarrow & \color{red}{330} x& = & 13 \\\Leftrightarrow & x = \frac{13}{330} & & \\ & V = \left\{ \frac{13}{330} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+16} & = & \color{red}{49x} +8 \\\Leftrightarrow & 56x \color{red}{+16} \color{blue}{-16} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-16} \\\Leftrightarrow & 56x-49x& = & 8-16 \\\Leftrightarrow & \color{red}{7} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{3})& = & -6x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{10}{3}& = & -6x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+110} & = & \color{red}{-198x} +6 \\\Leftrightarrow & 825x \color{red}{+110} \color{blue}{-110} \color{blue}{+198x} & = & \color{red}{-198x} +6 \color{blue}{+198x} \color{blue}{-110} \\\Leftrightarrow & 825x+198x& = & 6-110 \\\Leftrightarrow & \color{red}{1023} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{1023} & & \\ & V = \left\{ \frac{-104}{1023} \right\} & \\\end{align}\)