Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & -4x+\frac{5}{7} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{20}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-105} & = & \color{red}{-112x} +20 \\\Leftrightarrow & -420x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +20 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & -420x+112x& = & 20+105 \\\Leftrightarrow & \color{red}{-308} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-308} & & \\\Leftrightarrow & x = \frac{-125}{308} & & \\ & V = \left\{ \frac{-125}{308} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+20} & = & \color{red}{-154x} +33 \\\Leftrightarrow & -220x \color{red}{+20} \color{blue}{-20} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-20} \\\Leftrightarrow & -220x+154x& = & 33-20 \\\Leftrightarrow & \color{red}{-66} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-66} & & \\\Leftrightarrow & x = \frac{-13}{66} & & \\ & V = \left\{ \frac{-13}{66} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{+42} & = & \color{red}{-135x} +20 \\\Leftrightarrow & -525x \color{red}{+42} \color{blue}{-42} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{-42} \\\Leftrightarrow & -525x+135x& = & 20-42 \\\Leftrightarrow & \color{red}{-390} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-390} & & \\\Leftrightarrow & x = \frac{11}{195} & & \\ & V = \left\{ \frac{11}{195} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{-15} & = & \color{red}{-40x} +9 \\\Leftrightarrow & 96x \color{red}{-15} \color{blue}{+15} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{+15} \\\Leftrightarrow & 96x+40x& = & 9+15 \\\Leftrightarrow & \color{red}{136} x& = & 24 \\\Leftrightarrow & x = \frac{24}{136} & & \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{11})& = & 4x+\frac{3}{10} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{150}{ \color{blue}{110} })& = & (\frac{440}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-150} & = & \color{red}{440x} +33 \\\Leftrightarrow & -1650x \color{red}{-150} \color{blue}{+150} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{+150} \\\Leftrightarrow & -1650x-440x& = & 33+150 \\\Leftrightarrow & \color{red}{-2090} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-2090} & & \\\Leftrightarrow & x = \frac{-183}{2090} & & \\ & V = \left\{ \frac{-183}{2090} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{10})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{9}{10}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-99} & = & \color{red}{-550x} +50 \\\Leftrightarrow & -1320x \color{red}{-99} \color{blue}{+99} \color{blue}{+550x} & = & \color{red}{-550x} +50 \color{blue}{+550x} \color{blue}{+99} \\\Leftrightarrow & -1320x+550x& = & 50+99 \\\Leftrightarrow & \color{red}{-770} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-770} & & \\\Leftrightarrow & x = \frac{-149}{770} & & \\ & V = \left\{ \frac{-149}{770} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{49x} +3 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-20} \\\Leftrightarrow & 140x-49x& = & 3-20 \\\Leftrightarrow & \color{red}{91} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{91} & & \\ & V = \left\{ \frac{-17}{91} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{5}{4} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-48} & = & \color{red}{-80x} +25 \\\Leftrightarrow & -300x \color{red}{-48} \color{blue}{+48} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{+48} \\\Leftrightarrow & -300x+80x& = & 25+48 \\\Leftrightarrow & \color{red}{-220} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-220} & & \\\Leftrightarrow & x = \frac{-73}{220} & & \\ & V = \left\{ \frac{-73}{220} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{3})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{10}{3}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+70} & = & \color{red}{63x} +30 \\\Leftrightarrow & 420x \color{red}{+70} \color{blue}{-70} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-70} \\\Leftrightarrow & 420x-63x& = & 30-70 \\\Leftrightarrow & \color{red}{357} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{357} & & \\ & V = \left\{ \frac{-40}{357} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+6} & = & \color{red}{49x} +6 \\\Leftrightarrow & 42x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 42x-49x& = & 6-6 \\\Leftrightarrow & \color{red}{-7} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-7} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{1}{2})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{5}{2}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-15} & = & \color{red}{12x} +16 \\\Leftrightarrow & 90x \color{red}{-15} \color{blue}{+15} \color{blue}{-12x} & = & \color{red}{12x} +16 \color{blue}{-12x} \color{blue}{+15} \\\Leftrightarrow & 90x-12x& = & 16+15 \\\Leftrightarrow & \color{red}{78} x& = & 31 \\\Leftrightarrow & x = \frac{31}{78} & & \\ & V = \left\{ \frac{31}{78} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{8})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{15}{8}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{+165} & = & \color{red}{264x} +80 \\\Leftrightarrow & 1760x \color{red}{+165} \color{blue}{-165} \color{blue}{-264x} & = & \color{red}{264x} +80 \color{blue}{-264x} \color{blue}{-165} \\\Leftrightarrow & 1760x-264x& = & 80-165 \\\Leftrightarrow & \color{red}{1496} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{1496} & & \\\Leftrightarrow & x = \frac{-5}{88} & & \\ & V = \left\{ \frac{-5}{88} \right\} & \\\end{align}\)