Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-20} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 220x \color{red}{-20} \color{blue}{+20} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+20} \\\Leftrightarrow & 220x+154x& = & 77+20 \\\Leftrightarrow & \color{red}{374} x& = & 97 \\\Leftrightarrow & x = \frac{97}{374} & & \\ & V = \left\{ \frac{97}{374} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & 2x+\frac{5}{7} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 2x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{-196} & = & \color{red}{126x} +45 \\\Leftrightarrow & -1764x \color{red}{-196} \color{blue}{+196} \color{blue}{-126x} & = & \color{red}{126x} +45 \color{blue}{-126x} \color{blue}{+196} \\\Leftrightarrow & -1764x-126x& = & 45+196 \\\Leftrightarrow & \color{red}{-1890} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-1890} & & \\\Leftrightarrow & x = \frac{-241}{1890} & & \\ & V = \left\{ \frac{-241}{1890} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & 8x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-180} & = & \color{red}{504x} +70 \\\Leftrightarrow & 945x \color{red}{-180} \color{blue}{+180} \color{blue}{-504x} & = & \color{red}{504x} +70 \color{blue}{-504x} \color{blue}{+180} \\\Leftrightarrow & 945x-504x& = & 70+180 \\\Leftrightarrow & \color{red}{441} x& = & 250 \\\Leftrightarrow & x = \frac{250}{441} & & \\ & V = \left\{ \frac{250}{441} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{3})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+24} & = & \color{red}{81x} +2 \\\Leftrightarrow & -72x \color{red}{+24} \color{blue}{-24} \color{blue}{-81x} & = & \color{red}{81x} +2 \color{blue}{-81x} \color{blue}{-24} \\\Leftrightarrow & -72x-81x& = & 2-24 \\\Leftrightarrow & \color{red}{-153} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-153} & & \\\Leftrightarrow & x = \frac{22}{153} & & \\ & V = \left\{ \frac{22}{153} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+36} & = & \color{red}{-105x} +28 \\\Leftrightarrow & 252x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 252x+105x& = & 28-36 \\\Leftrightarrow & \color{red}{357} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{357} & & \\ & V = \left\{ \frac{-8}{357} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{11})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{16}{11}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-80} & = & \color{red}{-275x} +22 \\\Leftrightarrow & -660x \color{red}{-80} \color{blue}{+80} \color{blue}{+275x} & = & \color{red}{-275x} +22 \color{blue}{+275x} \color{blue}{+80} \\\Leftrightarrow & -660x+275x& = & 22+80 \\\Leftrightarrow & \color{red}{-385} x& = & 102 \\\Leftrightarrow & x = \frac{102}{-385} & & \\\Leftrightarrow & x = \frac{-102}{385} & & \\ & V = \left\{ \frac{-102}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{9})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 4x+\frac{10}{9}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+110} & = & \color{red}{495x} +72 \\\Leftrightarrow & 396x \color{red}{+110} \color{blue}{-110} \color{blue}{-495x} & = & \color{red}{495x} +72 \color{blue}{-495x} \color{blue}{-110} \\\Leftrightarrow & 396x-495x& = & 72-110 \\\Leftrightarrow & \color{red}{-99} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-99} & & \\\Leftrightarrow & x = \frac{38}{99} & & \\ & V = \left\{ \frac{38}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{-45} & = & \color{red}{120x} +28 \\\Leftrightarrow & 288x \color{red}{-45} \color{blue}{+45} \color{blue}{-120x} & = & \color{red}{120x} +28 \color{blue}{-120x} \color{blue}{+45} \\\Leftrightarrow & 288x-120x& = & 28+45 \\\Leftrightarrow & \color{red}{168} x& = & 73 \\\Leftrightarrow & x = \frac{73}{168} & & \\ & V = \left\{ \frac{73}{168} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-90} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -990x \color{red}{-90} \color{blue}{+90} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+90} \\\Leftrightarrow & -990x+495x& = & 22+90 \\\Leftrightarrow & \color{red}{-495} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-495} & & \\\Leftrightarrow & x = \frac{-112}{495} & & \\ & V = \left\{ \frac{-112}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 252x+105x& = & 14+90 \\\Leftrightarrow & \color{red}{357} x& = & 104 \\\Leftrightarrow & x = \frac{104}{357} & & \\ & V = \left\{ \frac{104}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{539x} +56 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{+330} \\\Leftrightarrow & 1848x-539x& = & 56+330 \\\Leftrightarrow & \color{red}{1309} x& = & 386 \\\Leftrightarrow & x = \frac{386}{1309} & & \\ & V = \left\{ \frac{386}{1309} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -28x-\frac{28}{11}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x- \frac{112}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{-112} & = & \color{red}{-396x} +33 \\\Leftrightarrow & -1232x \color{red}{-112} \color{blue}{+112} \color{blue}{+396x} & = & \color{red}{-396x} +33 \color{blue}{+396x} \color{blue}{+112} \\\Leftrightarrow & -1232x+396x& = & 33+112 \\\Leftrightarrow & \color{red}{-836} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-836} & & \\\Leftrightarrow & x = \frac{-145}{836} & & \\ & V = \left\{ \frac{-145}{836} \right\} & \\\end{align}\)