Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{11})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 35x+\frac{21}{11}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+21} & = & \color{red}{22x} +2 \\\Leftrightarrow & 385x \color{red}{+21} \color{blue}{-21} \color{blue}{-22x} & = & \color{red}{22x} +2 \color{blue}{-22x} \color{blue}{-21} \\\Leftrightarrow & 385x-22x& = & 2-21 \\\Leftrightarrow & \color{red}{363} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{363} & & \\ & V = \left\{ \frac{-19}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{105x} +6 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{+98} \\\Leftrightarrow & 588x-105x& = & 6+98 \\\Leftrightarrow & \color{red}{483} x& = & 104 \\\Leftrightarrow & x = \frac{104}{483} & & \\ & V = \left\{ \frac{104}{483} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{+72} & = & \color{red}{308x} +55 \\\Leftrightarrow & -1320x \color{red}{+72} \color{blue}{-72} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{-72} \\\Leftrightarrow & -1320x-308x& = & 55-72 \\\Leftrightarrow & \color{red}{-1628} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1628} & & \\\Leftrightarrow & x = \frac{17}{1628} & & \\ & V = \left\{ \frac{17}{1628} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -420x+175x& = & 10-84 \\\Leftrightarrow & \color{red}{-245} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-245} & & \\\Leftrightarrow & x = \frac{74}{245} & & \\ & V = \left\{ \frac{74}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{21x} +10 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 45x-21x& = & 10+20 \\\Leftrightarrow & \color{red}{24} x& = & 30 \\\Leftrightarrow & x = \frac{30}{24} & & \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+1)& = & 7x+\frac{10}{7} \\\Leftrightarrow & 20x-5& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{35}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-35} & = & \color{red}{49x} +10 \\\Leftrightarrow & 140x \color{red}{-35} \color{blue}{+35} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+35} \\\Leftrightarrow & 140x-49x& = & 10+35 \\\Leftrightarrow & \color{red}{91} x& = & 45 \\\Leftrightarrow & x = \frac{45}{91} & & \\ & V = \left\{ \frac{45}{91} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{120x} +48 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-120x} & = & \color{red}{120x} +48 \color{blue}{-120x} \color{blue}{-105} \\\Leftrightarrow & -1400x-120x& = & 48-105 \\\Leftrightarrow & \color{red}{-1520} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-1520} & & \\\Leftrightarrow & x = \frac{3}{80} & & \\ & V = \left\{ \frac{3}{80} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-8} & = & \color{red}{63x} +12 \\\Leftrightarrow & -180x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -180x-63x& = & 12+8 \\\Leftrightarrow & \color{red}{-243} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-243} & & \\\Leftrightarrow & x = \frac{-20}{243} & & \\ & V = \left\{ \frac{-20}{243} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-40} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -270x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & -270x+315x& = & 54+40 \\\Leftrightarrow & \color{red}{45} x& = & 94 \\\Leftrightarrow & x = \frac{94}{45} & & \\ & V = \left\{ \frac{94}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{11})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{-270} & = & \color{red}{-495x} +55 \\\Leftrightarrow & 1782x \color{red}{-270} \color{blue}{+270} \color{blue}{+495x} & = & \color{red}{-495x} +55 \color{blue}{+495x} \color{blue}{+270} \\\Leftrightarrow & 1782x+495x& = & 55+270 \\\Leftrightarrow & \color{red}{2277} x& = & 325 \\\Leftrightarrow & x = \frac{325}{2277} & & \\ & V = \left\{ \frac{325}{2277} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 14-18 \\\Leftrightarrow & \color{red}{-273} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-273} & & \\\Leftrightarrow & x = \frac{4}{273} & & \\ & V = \left\{ \frac{4}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 9x+\frac{7}{11} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-176} & = & \color{red}{693x} +49 \\\Leftrightarrow & 1540x \color{red}{-176} \color{blue}{+176} \color{blue}{-693x} & = & \color{red}{693x} +49 \color{blue}{-693x} \color{blue}{+176} \\\Leftrightarrow & 1540x-693x& = & 49+176 \\\Leftrightarrow & \color{red}{847} x& = & 225 \\\Leftrightarrow & x = \frac{225}{847} & & \\ & V = \left\{ \frac{225}{847} \right\} & \\\end{align}\)