Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+15}& = & -7 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-15x } & = & -7 \color{red}{ +15x }\color{blue}{-15-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-22\\\Leftrightarrow & \color{red}{-16}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-12}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-6x } & = & -15 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-3x } & = & 6 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+15}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-10x } & = & 3 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+13}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-13x } & = & 5 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-15}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-3x } & = & 11 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-17x & = &26\\\Leftrightarrow & \color{red}{-17}x & = &26\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{26}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{17} } & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-5}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5+7x } & = & 11 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-10}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-9x } & = & -8 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)