Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{11})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 28x+\frac{35}{11}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{+280} & = & \color{red}{792x} +55 \\\Leftrightarrow & 2464x \color{red}{+280} \color{blue}{-280} \color{blue}{-792x} & = & \color{red}{792x} +55 \color{blue}{-792x} \color{blue}{-280} \\\Leftrightarrow & 2464x-792x& = & 55-280 \\\Leftrightarrow & \color{red}{1672} x& = & -225 \\\Leftrightarrow & x = \frac{-225}{1672} & & \\ & V = \left\{ \frac{-225}{1672} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-8} & = & \color{red}{63x} +30 \\\Leftrightarrow & 72x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & 72x-63x& = & 30+8 \\\Leftrightarrow & \color{red}{9} x& = & 38 \\\Leftrightarrow & x = \frac{38}{9} & & \\ & V = \left\{ \frac{38}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & 560x+245x& = & 42+100 \\\Leftrightarrow & \color{red}{805} x& = & 142 \\\Leftrightarrow & x = \frac{142}{805} & & \\ & V = \left\{ \frac{142}{805} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{4})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{21}{4}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-140}{ \color{blue}{4} }x- \frac{21}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -140x \color{red}{-21} & = & \color{red}{-12x} +18 \\\Leftrightarrow & -140x \color{red}{-21} \color{blue}{+21} \color{blue}{+12x} & = & \color{red}{-12x} +18 \color{blue}{+12x} \color{blue}{+21} \\\Leftrightarrow & -140x+12x& = & 18+21 \\\Leftrightarrow & \color{red}{-128} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-128} & & \\\Leftrightarrow & x = \frac{-39}{128} & & \\ & V = \left\{ \frac{-39}{128} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 28x+\frac{21}{8}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{+147} & = & \color{red}{-504x} +80 \\\Leftrightarrow & 1568x \color{red}{+147} \color{blue}{-147} \color{blue}{+504x} & = & \color{red}{-504x} +80 \color{blue}{+504x} \color{blue}{-147} \\\Leftrightarrow & 1568x+504x& = & 80-147 \\\Leftrightarrow & \color{red}{2072} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{2072} & & \\ & V = \left\{ \frac{-67}{2072} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x+\frac{18}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{198}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+198} & = & \color{red}{385x} +42 \\\Leftrightarrow & 1386x \color{red}{+198} \color{blue}{-198} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-198} \\\Leftrightarrow & 1386x-385x& = & 42-198 \\\Leftrightarrow & \color{red}{1001} x& = & -156 \\\Leftrightarrow & x = \frac{-156}{1001} & & \\\Leftrightarrow & x = \frac{-12}{77} & & \\ & V = \left\{ \frac{-12}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1890x \color{red}{-270} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 1890x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & 1890x+441x& = & 14+270 \\\Leftrightarrow & \color{red}{2331} x& = & 284 \\\Leftrightarrow & x = \frac{284}{2331} & & \\ & V = \left\{ \frac{284}{2331} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{126}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-126} & = & \color{red}{-405x} +50 \\\Leftrightarrow & -1260x \color{red}{-126} \color{blue}{+126} \color{blue}{+405x} & = & \color{red}{-405x} +50 \color{blue}{+405x} \color{blue}{+126} \\\Leftrightarrow & -1260x+405x& = & 50+126 \\\Leftrightarrow & \color{red}{-855} x& = & 176 \\\Leftrightarrow & x = \frac{176}{-855} & & \\\Leftrightarrow & x = \frac{-176}{855} & & \\ & V = \left\{ \frac{-176}{855} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & -990x+231x& = & 110+54 \\\Leftrightarrow & \color{red}{-759} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-759} & & \\\Leftrightarrow & x = \frac{-164}{759} & & \\ & V = \left\{ \frac{-164}{759} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+75} & = & \color{red}{100x} +24 \\\Leftrightarrow & -240x \color{red}{+75} \color{blue}{-75} \color{blue}{-100x} & = & \color{red}{100x} +24 \color{blue}{-100x} \color{blue}{-75} \\\Leftrightarrow & -240x-100x& = & 24-75 \\\Leftrightarrow & \color{red}{-340} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-340} & & \\\Leftrightarrow & x = \frac{3}{20} & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{9})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{45}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{+80} & = & \color{red}{108x} +45 \\\Leftrightarrow & 720x \color{red}{+80} \color{blue}{-80} \color{blue}{-108x} & = & \color{red}{108x} +45 \color{blue}{-108x} \color{blue}{-80} \\\Leftrightarrow & 720x-108x& = & 45-80 \\\Leftrightarrow & \color{red}{612} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{612} & & \\ & V = \left\{ \frac{-35}{612} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{9})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 10x+\frac{20}{9}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+220} & = & \color{red}{693x} +72 \\\Leftrightarrow & 990x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +72 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & 990x-693x& = & 72-220 \\\Leftrightarrow & \color{red}{297} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{297} & & \\ & V = \left\{ \frac{-148}{297} \right\} & \\\end{align}\)