Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{9})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{-45x} +5 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{+45x} & = & \color{red}{-45x} +5 \color{blue}{+45x} \color{blue}{-8} \\\Leftrightarrow & -36x+45x& = & 5-8 \\\Leftrightarrow & \color{red}{9} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{9} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{-24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & 160x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 160x+50x& = & 35+24 \\\Leftrightarrow & \color{red}{210} x& = & 59 \\\Leftrightarrow & x = \frac{59}{210} & & \\ & V = \left\{ \frac{59}{210} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -135x+105x& = & 20-36 \\\Leftrightarrow & \color{red}{-30} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-30} & & \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{7})& = & 8x+\frac{9}{11} \\\Leftrightarrow & 9x-\frac{15}{7}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-165} & = & \color{red}{616x} +63 \\\Leftrightarrow & 693x \color{red}{-165} \color{blue}{+165} \color{blue}{-616x} & = & \color{red}{616x} +63 \color{blue}{-616x} \color{blue}{+165} \\\Leftrightarrow & 693x-616x& = & 63+165 \\\Leftrightarrow & \color{red}{77} x& = & 228 \\\Leftrightarrow & x = \frac{228}{77} & & \\ & V = \left\{ \frac{228}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{4})& = & -8x+\frac{9}{2} \\\Leftrightarrow & 35x-\frac{35}{4}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{140}{ \color{blue}{4} }x- \frac{35}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 140x \color{red}{-35} & = & \color{red}{-32x} +18 \\\Leftrightarrow & 140x \color{red}{-35} \color{blue}{+35} \color{blue}{+32x} & = & \color{red}{-32x} +18 \color{blue}{+32x} \color{blue}{+35} \\\Leftrightarrow & 140x+32x& = & 18+35 \\\Leftrightarrow & \color{red}{172} x& = & 53 \\\Leftrightarrow & x = \frac{53}{172} & & \\ & V = \left\{ \frac{53}{172} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -14x+\frac{28}{3}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{+196} & = & \color{red}{63x} +27 \\\Leftrightarrow & -294x \color{red}{+196} \color{blue}{-196} \color{blue}{-63x} & = & \color{red}{63x} +27 \color{blue}{-63x} \color{blue}{-196} \\\Leftrightarrow & -294x-63x& = & 27-196 \\\Leftrightarrow & \color{red}{-357} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-357} & & \\\Leftrightarrow & x = \frac{169}{357} & & \\ & V = \left\{ \frac{169}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-70} & = & \color{red}{120x} +9 \\\Leftrightarrow & -315x \color{red}{-70} \color{blue}{+70} \color{blue}{-120x} & = & \color{red}{120x} +9 \color{blue}{-120x} \color{blue}{+70} \\\Leftrightarrow & -315x-120x& = & 9+70 \\\Leftrightarrow & \color{red}{-435} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-435} & & \\\Leftrightarrow & x = \frac{-79}{435} & & \\ & V = \left\{ \frac{-79}{435} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-216x} +80 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & 336x+216x& = & 80-63 \\\Leftrightarrow & \color{red}{552} x& = & 17 \\\Leftrightarrow & x = \frac{17}{552} & & \\ & V = \left\{ \frac{17}{552} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{7})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-10} & = & \color{red}{21x} +10 \\\Leftrightarrow & -56x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & -56x-21x& = & 10+10 \\\Leftrightarrow & \color{red}{-77} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-77} & & \\\Leftrightarrow & x = \frac{-20}{77} & & \\ & V = \left\{ \frac{-20}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 30x+\frac{12}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{+24} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 420x \color{red}{+24} \color{blue}{-24} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-24} \\\Leftrightarrow & 420x+98x& = & 21-24 \\\Leftrightarrow & \color{red}{518} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{518} & & \\ & V = \left\{ \frac{-3}{518} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-1)& = & -7x+\frac{3}{10} \\\Leftrightarrow & -20x+5& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x+ \frac{50}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{+50} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -200x \color{red}{+50} \color{blue}{-50} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-50} \\\Leftrightarrow & -200x+70x& = & 3-50 \\\Leftrightarrow & \color{red}{-130} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-130} & & \\\Leftrightarrow & x = \frac{47}{130} & & \\ & V = \left\{ \frac{47}{130} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{5})& = & -8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{28}{5}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-420}{ \color{blue}{20} }x- \frac{112}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -420x \color{red}{-112} & = & \color{red}{-160x} +45 \\\Leftrightarrow & -420x \color{red}{-112} \color{blue}{+112} \color{blue}{+160x} & = & \color{red}{-160x} +45 \color{blue}{+160x} \color{blue}{+112} \\\Leftrightarrow & -420x+160x& = & 45+112 \\\Leftrightarrow & \color{red}{-260} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-260} & & \\\Leftrightarrow & x = \frac{-157}{260} & & \\ & V = \left\{ \frac{-157}{260} \right\} & \\\end{align}\)