Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 7x+\frac{3}{5} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-50} & = & \color{red}{245x} +21 \\\Leftrightarrow & 700x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +21 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & 700x-245x& = & 21+50 \\\Leftrightarrow & \color{red}{455} x& = & 71 \\\Leftrightarrow & x = \frac{71}{455} & & \\ & V = \left\{ \frac{71}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -210x+147x& = & 14-30 \\\Leftrightarrow & \color{red}{-63} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-63} & & \\\Leftrightarrow & x = \frac{16}{63} & & \\ & V = \left\{ \frac{16}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+6} & = & \color{red}{49x} +3 \\\Leftrightarrow & 105x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 105x-49x& = & 3-6 \\\Leftrightarrow & \color{red}{56} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{56} & & \\ & V = \left\{ \frac{-3}{56} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 28x+4& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{12}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+12} & = & \color{red}{27x} +8 \\\Leftrightarrow & 84x \color{red}{+12} \color{blue}{-12} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-12} \\\Leftrightarrow & 84x-27x& = & 8-12 \\\Leftrightarrow & \color{red}{57} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{57} & & \\ & V = \left\{ \frac{-4}{57} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x- \frac{24}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{100x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+24} \\\Leftrightarrow & 120x-100x& = & 45+24 \\\Leftrightarrow & \color{red}{20} x& = & 69 \\\Leftrightarrow & x = \frac{69}{20} & & \\ & V = \left\{ \frac{69}{20} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-8} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -54x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -54x+63x& = & 4+8 \\\Leftrightarrow & \color{red}{9} x& = & 12 \\\Leftrightarrow & x = \frac{12}{9} & & \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-88}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{-88x} +24 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{+88x} & = & \color{red}{-88x} +24 \color{blue}{+88x} \color{blue}{+165} \\\Leftrightarrow & 396x+88x& = & 24+165 \\\Leftrightarrow & \color{red}{484} x& = & 189 \\\Leftrightarrow & x = \frac{189}{484} & & \\ & V = \left\{ \frac{189}{484} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{-60} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 252x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & 252x+70x& = & 63+60 \\\Leftrightarrow & \color{red}{322} x& = & 123 \\\Leftrightarrow & x = \frac{123}{322} & & \\ & V = \left\{ \frac{123}{322} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{+4} & = & \color{red}{-45x} +2 \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & -20x+45x& = & 2-4 \\\Leftrightarrow & \color{red}{25} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{+100} & = & \color{red}{-210x} +63 \\\Leftrightarrow & 280x \color{red}{+100} \color{blue}{-100} \color{blue}{+210x} & = & \color{red}{-210x} +63 \color{blue}{+210x} \color{blue}{-100} \\\Leftrightarrow & 280x+210x& = & 63-100 \\\Leftrightarrow & \color{red}{490} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{490} & & \\ & V = \left\{ \frac{-37}{490} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{255} x& = & 4 \\\Leftrightarrow & x = \frac{4}{255} & & \\ & V = \left\{ \frac{4}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{5})& = & 8x+\frac{5}{12} \\\Leftrightarrow & -21x-\frac{14}{5}& = & 8x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1260}{ \color{blue}{60} }x- \frac{168}{ \color{blue}{60} })& = & (\frac{480}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1260x \color{red}{-168} & = & \color{red}{480x} +25 \\\Leftrightarrow & -1260x \color{red}{-168} \color{blue}{+168} \color{blue}{-480x} & = & \color{red}{480x} +25 \color{blue}{-480x} \color{blue}{+168} \\\Leftrightarrow & -1260x-480x& = & 25+168 \\\Leftrightarrow & \color{red}{-1740} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-1740} & & \\\Leftrightarrow & x = \frac{-193}{1740} & & \\ & V = \left\{ \frac{-193}{1740} \right\} & \\\end{align}\)