Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{9}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-99} & = & \color{red}{539x} +14 \\\Leftrightarrow & 924x \color{red}{-99} \color{blue}{+99} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{+99} \\\Leftrightarrow & 924x-539x& = & 14+99 \\\Leftrightarrow & \color{red}{385} x& = & 113 \\\Leftrightarrow & x = \frac{113}{385} & & \\ & V = \left\{ \frac{113}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & -4x+\frac{5}{7} \\\Leftrightarrow & -35x-\frac{14}{11}& = & -4x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x- \frac{98}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{-98} & = & \color{red}{-308x} +55 \\\Leftrightarrow & -2695x \color{red}{-98} \color{blue}{+98} \color{blue}{+308x} & = & \color{red}{-308x} +55 \color{blue}{+308x} \color{blue}{+98} \\\Leftrightarrow & -2695x+308x& = & 55+98 \\\Leftrightarrow & \color{red}{-2387} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-2387} & & \\\Leftrightarrow & x = \frac{-153}{2387} & & \\ & V = \left\{ \frac{-153}{2387} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-126} & = & \color{red}{-175x} +45 \\\Leftrightarrow & 420x \color{red}{-126} \color{blue}{+126} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{+126} \\\Leftrightarrow & 420x+175x& = & 45+126 \\\Leftrightarrow & \color{red}{595} x& = & 171 \\\Leftrightarrow & x = \frac{171}{595} & & \\ & V = \left\{ \frac{171}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+162} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 1188x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & 1188x+495x& = & 88-162 \\\Leftrightarrow & \color{red}{1683} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1683} & & \\ & V = \left\{ \frac{-74}{1683} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{-77x} +4 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{-18} \\\Leftrightarrow & -330x+77x& = & 4-18 \\\Leftrightarrow & \color{red}{-253} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-253} & & \\\Leftrightarrow & x = \frac{14}{253} & & \\ & V = \left\{ \frac{14}{253} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{9})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-44} & = & \color{red}{693x} +90 \\\Leftrightarrow & -594x \color{red}{-44} \color{blue}{+44} \color{blue}{-693x} & = & \color{red}{693x} +90 \color{blue}{-693x} \color{blue}{+44} \\\Leftrightarrow & -594x-693x& = & 90+44 \\\Leftrightarrow & \color{red}{-1287} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-1287} & & \\\Leftrightarrow & x = \frac{-134}{1287} & & \\ & V = \left\{ \frac{-134}{1287} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+48} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -264x \color{red}{+48} \color{blue}{-48} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-48} \\\Leftrightarrow & -264x+110x& = & 33-48 \\\Leftrightarrow & \color{red}{-154} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-154} & & \\\Leftrightarrow & x = \frac{15}{154} & & \\ & V = \left\{ \frac{15}{154} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{2})& = & 8x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{9}{2}& = & 8x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+99} & = & \color{red}{176x} +14 \\\Leftrightarrow & -330x \color{red}{+99} \color{blue}{-99} \color{blue}{-176x} & = & \color{red}{176x} +14 \color{blue}{-176x} \color{blue}{-99} \\\Leftrightarrow & -330x-176x& = & 14-99 \\\Leftrightarrow & \color{red}{-506} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-506} & & \\\Leftrightarrow & x = \frac{85}{506} & & \\ & V = \left\{ \frac{85}{506} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{1}{2})& = & -4x+\frac{3}{7} \\\Leftrightarrow & -28x-\frac{7}{2}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-392}{ \color{blue}{14} }x- \frac{49}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -392x \color{red}{-49} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -392x \color{red}{-49} \color{blue}{+49} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{+49} \\\Leftrightarrow & -392x+56x& = & 6+49 \\\Leftrightarrow & \color{red}{-336} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-336} & & \\\Leftrightarrow & x = \frac{-55}{336} & & \\ & V = \left\{ \frac{-55}{336} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & 3x+\frac{8}{5} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+50} & = & \color{red}{105x} +56 \\\Leftrightarrow & -875x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -875x-105x& = & 56-50 \\\Leftrightarrow & \color{red}{-980} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-980} & & \\\Leftrightarrow & x = \frac{-3}{490} & & \\ & V = \left\{ \frac{-3}{490} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{12}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{+120} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -660x \color{red}{+120} \color{blue}{-120} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{-120} \\\Leftrightarrow & -660x+770x& = & 99-120 \\\Leftrightarrow & \color{red}{110} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{110} & & \\ & V = \left\{ \frac{-21}{110} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1680}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1680x \color{red}{-300} & = & \color{red}{350x} +63 \\\Leftrightarrow & -1680x \color{red}{-300} \color{blue}{+300} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{+300} \\\Leftrightarrow & -1680x-350x& = & 63+300 \\\Leftrightarrow & \color{red}{-2030} x& = & 363 \\\Leftrightarrow & x = \frac{363}{-2030} & & \\\Leftrightarrow & x = \frac{-363}{2030} & & \\ & V = \left\{ \frac{-363}{2030} \right\} & \\\end{align}\)