Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & -9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-13x } & = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+15}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-7x } & = & -4 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-8}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-10x } & = & 10 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+5}& = & 12 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-12x } & = & 12 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-23x & = &7\\\Leftrightarrow & \color{red}{-23}x & = &7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-6}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+11x } & = & 9 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &20x & = &15\\\Leftrightarrow & \color{red}{20}x & = &15\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{15}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)