Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(4x-2=15-15x\)
2. \(15x+11=-5-7x\)
3. \(-5x+10=-12+3x\)
4. \(-8x+4=-10+9x\)
5. \(-12x+3=-15+x\)
6. \(-7x+1=-2+x\)
7. \(3x-6=13-5x\)
8. \(14x+9=14-9x\)
9. \(-10x+6=-7+11x\)
10. \(-14x+4=13+x\)
11. \(9x-2=-9+x\)
12. \(6x+13=-4+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-2}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+15x } & = & 15 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+11}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+7x } & = & -5 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &22x & = &-16\\\Leftrightarrow & \color{red}{22}x & = &-16\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-16}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+10}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-3x } & = & -12 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-22\\\Leftrightarrow & \color{red}{-8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+4}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-9x } & = & -10 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-14\\\Leftrightarrow & \color{red}{-17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-6}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6+5x } & = & 13 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+9}& = & 14 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+9x } & = & 14 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &23x & = &5\\\Leftrightarrow & \color{red}{23}x & = &5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+6}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-11x } & = & -7 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-21x & = &-13\\\Leftrightarrow & \color{red}{-21}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-13}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{13}{21} } & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & -9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)