Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x-\frac{15}{4}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-45} & = & \color{red}{-60x} +10 \\\Leftrightarrow & 144x \color{red}{-45} \color{blue}{+45} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{+45} \\\Leftrightarrow & 144x+60x& = & 10+45 \\\Leftrightarrow & \color{red}{204} x& = & 55 \\\Leftrightarrow & x = \frac{55}{204} & & \\ & V = \left\{ \frac{55}{204} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{8})& = & -6x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -6x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-240}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+105} & = & \color{red}{-240x} +48 \\\Leftrightarrow & -1120x \color{red}{+105} \color{blue}{-105} \color{blue}{+240x} & = & \color{red}{-240x} +48 \color{blue}{+240x} \color{blue}{-105} \\\Leftrightarrow & -1120x+240x& = & 48-105 \\\Leftrightarrow & \color{red}{-880} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-880} & & \\\Leftrightarrow & x = \frac{57}{880} & & \\ & V = \left\{ \frac{57}{880} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -9x+\frac{7}{4} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+64} & = & \color{red}{-252x} +49 \\\Leftrightarrow & 560x \color{red}{+64} \color{blue}{-64} \color{blue}{+252x} & = & \color{red}{-252x} +49 \color{blue}{+252x} \color{blue}{-64} \\\Leftrightarrow & 560x+252x& = & 49-64 \\\Leftrightarrow & \color{red}{812} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{812} & & \\ & V = \left\{ \frac{-15}{812} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{2}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{75}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+75} & = & \color{red}{-42x} +4 \\\Leftrightarrow & -60x \color{red}{+75} \color{blue}{-75} \color{blue}{+42x} & = & \color{red}{-42x} +4 \color{blue}{+42x} \color{blue}{-75} \\\Leftrightarrow & -60x+42x& = & 4-75 \\\Leftrightarrow & \color{red}{-18} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-18} & & \\\Leftrightarrow & x = \frac{71}{18} & & \\ & V = \left\{ \frac{71}{18} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{-550x} +99 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{-120} \\\Leftrightarrow & 1320x+550x& = & 99-120 \\\Leftrightarrow & \color{red}{1870} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{1870} & & \\ & V = \left\{ \frac{-21}{1870} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 10x-\frac{6}{11}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-12} & = & \color{red}{198x} +33 \\\Leftrightarrow & 220x \color{red}{-12} \color{blue}{+12} \color{blue}{-198x} & = & \color{red}{198x} +33 \color{blue}{-198x} \color{blue}{+12} \\\Leftrightarrow & 220x-198x& = & 33+12 \\\Leftrightarrow & \color{red}{22} x& = & 45 \\\Leftrightarrow & x = \frac{45}{22} & & \\ & V = \left\{ \frac{45}{22} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+150} & = & \color{red}{140x} +42 \\\Leftrightarrow & -630x \color{red}{+150} \color{blue}{-150} \color{blue}{-140x} & = & \color{red}{140x} +42 \color{blue}{-140x} \color{blue}{-150} \\\Leftrightarrow & -630x-140x& = & 42-150 \\\Leftrightarrow & \color{red}{-770} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-770} & & \\\Leftrightarrow & x = \frac{54}{385} & & \\ & V = \left\{ \frac{54}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -8x-\frac{8}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{-32} & = & \color{red}{396x} +33 \\\Leftrightarrow & -352x \color{red}{-32} \color{blue}{+32} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{+32} \\\Leftrightarrow & -352x-396x& = & 33+32 \\\Leftrightarrow & \color{red}{-748} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-748} & & \\\Leftrightarrow & x = \frac{-65}{748} & & \\ & V = \left\{ \frac{-65}{748} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{4}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+36} \\\Leftrightarrow & 270x+225x& = & 25+36 \\\Leftrightarrow & \color{red}{495} x& = & 61 \\\Leftrightarrow & x = \frac{61}{495} & & \\ & V = \left\{ \frac{61}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+24} & = & \color{red}{110x} +55 \\\Leftrightarrow & -264x \color{red}{+24} \color{blue}{-24} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{-24} \\\Leftrightarrow & -264x-110x& = & 55-24 \\\Leftrightarrow & \color{red}{-374} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-374} & & \\\Leftrightarrow & x = \frac{-31}{374} & & \\ & V = \left\{ \frac{-31}{374} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+16} & = & \color{red}{21x} +2 \\\Leftrightarrow & 56x \color{red}{+16} \color{blue}{-16} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-16} \\\Leftrightarrow & 56x-21x& = & 2-16 \\\Leftrightarrow & \color{red}{35} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{35} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{9})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -20x+\frac{25}{9}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{275}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+275} & = & \color{red}{-297x} +81 \\\Leftrightarrow & -1980x \color{red}{+275} \color{blue}{-275} \color{blue}{+297x} & = & \color{red}{-297x} +81 \color{blue}{+297x} \color{blue}{-275} \\\Leftrightarrow & -1980x+297x& = & 81-275 \\\Leftrightarrow & \color{red}{-1683} x& = & -194 \\\Leftrightarrow & x = \frac{-194}{-1683} & & \\\Leftrightarrow & x = \frac{194}{1683} & & \\ & V = \left\{ \frac{194}{1683} \right\} & \\\end{align}\)