Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-9x} +2 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+9x} & = & \color{red}{-9x} +2 \color{blue}{+9x} \color{blue}{+8} \\\Leftrightarrow & -24x+9x& = & 2+8 \\\Leftrightarrow & \color{red}{-15} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-15} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{6}{11}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-30} & = & \color{red}{440x} +88 \\\Leftrightarrow & -825x \color{red}{-30} \color{blue}{+30} \color{blue}{-440x} & = & \color{red}{440x} +88 \color{blue}{-440x} \color{blue}{+30} \\\Leftrightarrow & -825x-440x& = & 88+30 \\\Leftrightarrow & \color{red}{-1265} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-1265} & & \\\Leftrightarrow & x = \frac{-118}{1265} & & \\ & V = \left\{ \frac{-118}{1265} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{+32} & = & \color{red}{-60x} +5 \\\Leftrightarrow & 48x \color{red}{+32} \color{blue}{-32} \color{blue}{+60x} & = & \color{red}{-60x} +5 \color{blue}{+60x} \color{blue}{-32} \\\Leftrightarrow & 48x+60x& = & 5-32 \\\Leftrightarrow & \color{red}{108} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{108} & & \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-42} & = & \color{red}{18x} +2 \\\Leftrightarrow & 189x \color{red}{-42} \color{blue}{+42} \color{blue}{-18x} & = & \color{red}{18x} +2 \color{blue}{-18x} \color{blue}{+42} \\\Leftrightarrow & 189x-18x& = & 2+42 \\\Leftrightarrow & \color{red}{171} x& = & 44 \\\Leftrightarrow & x = \frac{44}{171} & & \\ & V = \left\{ \frac{44}{171} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{16}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x+ \frac{80}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{+80} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 720x \color{red}{+80} \color{blue}{-80} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{-80} \\\Leftrightarrow & 720x+225x& = & 54-80 \\\Leftrightarrow & \color{red}{945} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{945} & & \\ & V = \left\{ \frac{-26}{945} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{10})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 14x-\frac{21}{10}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1540}{ \color{blue}{110} }x- \frac{231}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1540x \color{red}{-231} & = & \color{red}{-990x} +80 \\\Leftrightarrow & 1540x \color{red}{-231} \color{blue}{+231} \color{blue}{+990x} & = & \color{red}{-990x} +80 \color{blue}{+990x} \color{blue}{+231} \\\Leftrightarrow & 1540x+990x& = & 80+231 \\\Leftrightarrow & \color{red}{2530} x& = & 311 \\\Leftrightarrow & x = \frac{311}{2530} & & \\ & V = \left\{ \frac{311}{2530} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{9})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 16x-\frac{20}{9}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1152}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1152x \color{red}{-160} & = & \color{red}{-504x} +63 \\\Leftrightarrow & 1152x \color{red}{-160} \color{blue}{+160} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{+160} \\\Leftrightarrow & 1152x+504x& = & 63+160 \\\Leftrightarrow & \color{red}{1656} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1656} & & \\ & V = \left\{ \frac{223}{1656} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{11})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{10}{11}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-264}{ \color{blue}{66} }x- \frac{60}{ \color{blue}{66} })& = & (\frac{-594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -264x \color{red}{-60} & = & \color{red}{-594x} +55 \\\Leftrightarrow & -264x \color{red}{-60} \color{blue}{+60} \color{blue}{+594x} & = & \color{red}{-594x} +55 \color{blue}{+594x} \color{blue}{+60} \\\Leftrightarrow & -264x+594x& = & 55+60 \\\Leftrightarrow & \color{red}{330} x& = & 115 \\\Leftrightarrow & x = \frac{115}{330} & & \\\Leftrightarrow & x = \frac{23}{66} & & \\ & V = \left\{ \frac{23}{66} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{9})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{20}{9}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{+80} & = & \color{red}{-252x} +27 \\\Leftrightarrow & -360x \color{red}{+80} \color{blue}{-80} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{-80} \\\Leftrightarrow & -360x+252x& = & 27-80 \\\Leftrightarrow & \color{red}{-108} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-108} & & \\\Leftrightarrow & x = \frac{53}{108} & & \\ & V = \left\{ \frac{53}{108} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-45} & = & \color{red}{60x} +8 \\\Leftrightarrow & 144x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +8 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & 144x-60x& = & 8+45 \\\Leftrightarrow & \color{red}{84} x& = & 53 \\\Leftrightarrow & x = \frac{53}{84} & & \\ & V = \left\{ \frac{53}{84} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{9})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 21x+\frac{35}{9}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+35} & = & \color{red}{18x} +30 \\\Leftrightarrow & 189x \color{red}{+35} \color{blue}{-35} \color{blue}{-18x} & = & \color{red}{18x} +30 \color{blue}{-18x} \color{blue}{-35} \\\Leftrightarrow & 189x-18x& = & 30-35 \\\Leftrightarrow & \color{red}{171} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{171} & & \\ & V = \left\{ \frac{-5}{171} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -300x+105x& = & 10-36 \\\Leftrightarrow & \color{red}{-195} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-195} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)