Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-2}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-13x } & = & -8 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-11}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-10x } & = & -15 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-x } & = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-1}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-11x } & = & 5 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-1}& = & -13 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+12x } & = & -13 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+1}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+2x } & = & 3 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+9}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x } & = & 9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)