Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-4}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-4x } & = & -1 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+14}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-9x } & = & 2 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-24\\\Leftrightarrow & \color{red}{-9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+6}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-9x } & = & 7 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+2}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+3}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-4x } & = & 4 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & -2 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-16x & = &29\\\Leftrightarrow & \color{red}{-16}x & = &29\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{29}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{16} } & & \\ & V = \left\{ \frac{-29}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+12}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-13x } & = & 1 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+2}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & 4 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)