Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-6} & = & \color{red}{-44x} +4 \\\Leftrightarrow & 99x \color{red}{-6} \color{blue}{+6} \color{blue}{+44x} & = & \color{red}{-44x} +4 \color{blue}{+44x} \color{blue}{+6} \\\Leftrightarrow & 99x+44x& = & 4+6 \\\Leftrightarrow & \color{red}{143} x& = & 10 \\\Leftrightarrow & x = \frac{10}{143} & & \\ & V = \left\{ \frac{10}{143} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 1320x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 1320x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{1045} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1045} & & \\ & V = \left\{ \frac{-107}{1045} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+45} & = & \color{red}{168x} +80 \\\Leftrightarrow & 288x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +80 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & 288x-168x& = & 80-45 \\\Leftrightarrow & \color{red}{120} x& = & 35 \\\Leftrightarrow & x = \frac{35}{120} & & \\\Leftrightarrow & x = \frac{7}{24} & & \\ & V = \left\{ \frac{7}{24} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{11})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{175}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-175} & = & \color{red}{495x} +88 \\\Leftrightarrow & 1540x \color{red}{-175} \color{blue}{+175} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+175} \\\Leftrightarrow & 1540x-495x& = & 88+175 \\\Leftrightarrow & \color{red}{1045} x& = & 263 \\\Leftrightarrow & x = \frac{263}{1045} & & \\ & V = \left\{ \frac{263}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +44 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 44-54 \\\Leftrightarrow & \color{red}{-1221} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1221} & & \\\Leftrightarrow & x = \frac{10}{1221} & & \\ & V = \left\{ \frac{10}{1221} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{2})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{15}{2}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-105} & = & \color{red}{-98x} +8 \\\Leftrightarrow & 140x \color{red}{-105} \color{blue}{+105} \color{blue}{+98x} & = & \color{red}{-98x} +8 \color{blue}{+98x} \color{blue}{+105} \\\Leftrightarrow & 140x+98x& = & 8+105 \\\Leftrightarrow & \color{red}{238} x& = & 113 \\\Leftrightarrow & x = \frac{113}{238} & & \\ & V = \left\{ \frac{113}{238} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+54} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -270x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & -270x+315x& = & 20-54 \\\Leftrightarrow & \color{red}{45} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{45} & & \\ & V = \left\{ \frac{-34}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{12}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-36} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 495x \color{red}{-36} \color{blue}{+36} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+36} \\\Leftrightarrow & 495x+231x& = & 110+36 \\\Leftrightarrow & \color{red}{726} x& = & 146 \\\Leftrightarrow & x = \frac{146}{726} & & \\\Leftrightarrow & x = \frac{73}{363} & & \\ & V = \left\{ \frac{73}{363} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{20}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{80}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-80} & = & \color{red}{-308x} +99 \\\Leftrightarrow & -880x \color{red}{-80} \color{blue}{+80} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+80} \\\Leftrightarrow & -880x+308x& = & 99+80 \\\Leftrightarrow & \color{red}{-572} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-572} & & \\\Leftrightarrow & x = \frac{-179}{572} & & \\ & V = \left\{ \frac{-179}{572} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{8}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{189x} +56 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-24} \\\Leftrightarrow & -168x-189x& = & 56-24 \\\Leftrightarrow & \color{red}{-357} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-357} & & \\\Leftrightarrow & x = \frac{-32}{357} & & \\ & V = \left\{ \frac{-32}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -16x+\frac{20}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{+100} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -560x \color{red}{+100} \color{blue}{-100} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-100} \\\Leftrightarrow & -560x+245x& = & 28-100 \\\Leftrightarrow & \color{red}{-315} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-315} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{21}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+63} & = & \color{red}{99x} +88 \\\Leftrightarrow & -462x \color{red}{+63} \color{blue}{-63} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{-63} \\\Leftrightarrow & -462x-99x& = & 88-63 \\\Leftrightarrow & \color{red}{-561} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-561} & & \\\Leftrightarrow & x = \frac{-25}{561} & & \\ & V = \left\{ \frac{-25}{561} \right\} & \\\end{align}\)