Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{2})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -25x+\frac{15}{2}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{+45} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -150x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & -150x+42x& = & 5-45 \\\Leftrightarrow & \color{red}{-108} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-108} & & \\\Leftrightarrow & x = \frac{10}{27} & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+40} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -440x \color{red}{+40} \color{blue}{-40} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-40} \\\Leftrightarrow & -440x+495x& = & 22-40 \\\Leftrightarrow & \color{red}{55} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 28x+\frac{14}{9}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{28}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+28} & = & \color{red}{162x} +15 \\\Leftrightarrow & 504x \color{red}{+28} \color{blue}{-28} \color{blue}{-162x} & = & \color{red}{162x} +15 \color{blue}{-162x} \color{blue}{-28} \\\Leftrightarrow & 504x-162x& = & 15-28 \\\Leftrightarrow & \color{red}{342} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{342} & & \\ & V = \left\{ \frac{-13}{342} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{50x} +35 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{+18} \\\Leftrightarrow & 60x-50x& = & 35+18 \\\Leftrightarrow & \color{red}{10} x& = & 53 \\\Leftrightarrow & x = \frac{53}{10} & & \\ & V = \left\{ \frac{53}{10} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 8x+\frac{5}{4} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 8x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{160x} +25 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{-160x} & = & \color{red}{160x} +25 \color{blue}{-160x} \color{blue}{+48} \\\Leftrightarrow & 180x-160x& = & 25+48 \\\Leftrightarrow & \color{red}{20} x& = & 73 \\\Leftrightarrow & x = \frac{73}{20} & & \\ & V = \left\{ \frac{73}{20} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-330} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -924x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & -924x+385x& = & 42+330 \\\Leftrightarrow & \color{red}{-539} x& = & 372 \\\Leftrightarrow & x = \frac{372}{-539} & & \\\Leftrightarrow & x = \frac{-372}{539} & & \\ & V = \left\{ \frac{-372}{539} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{-162} & = & \color{red}{-693x} +55 \\\Leftrightarrow & 2970x \color{red}{-162} \color{blue}{+162} \color{blue}{+693x} & = & \color{red}{-693x} +55 \color{blue}{+693x} \color{blue}{+162} \\\Leftrightarrow & 2970x+693x& = & 55+162 \\\Leftrightarrow & \color{red}{3663} x& = & 217 \\\Leftrightarrow & x = \frac{217}{3663} & & \\ & V = \left\{ \frac{217}{3663} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{6}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-42} & = & \color{red}{-245x} +20 \\\Leftrightarrow & 350x \color{red}{-42} \color{blue}{+42} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{+42} \\\Leftrightarrow & 350x+245x& = & 20+42 \\\Leftrightarrow & \color{red}{595} x& = & 62 \\\Leftrightarrow & x = \frac{62}{595} & & \\ & V = \left\{ \frac{62}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{9}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{54}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{+54} \\\Leftrightarrow & -360x+150x& = & 25+54 \\\Leftrightarrow & \color{red}{-210} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-210} & & \\\Leftrightarrow & x = \frac{-79}{210} & & \\ & V = \left\{ \frac{-79}{210} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{6}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{+12} \\\Leftrightarrow & -60x+70x& = & 25+12 \\\Leftrightarrow & \color{red}{10} x& = & 37 \\\Leftrightarrow & x = \frac{37}{10} & & \\ & V = \left\{ \frac{37}{10} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-90} \\\Leftrightarrow & -990x+231x& = & 110-90 \\\Leftrightarrow & \color{red}{-759} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-759} & & \\\Leftrightarrow & x = \frac{-20}{759} & & \\ & V = \left\{ \frac{-20}{759} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-14} & = & \color{red}{72x} +4 \\\Leftrightarrow & -189x \color{red}{-14} \color{blue}{+14} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{+14} \\\Leftrightarrow & -189x-72x& = & 4+14 \\\Leftrightarrow & \color{red}{-261} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-261} & & \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)