Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+15}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-8x } & = & 5 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-15}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-13x } & = & -6 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+1}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-5x } & = & 6 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+15}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+7x } & = & 15 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-14}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-11x } & = & 3 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-21x & = &17\\\Leftrightarrow & \color{red}{-21}x & = &17\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{17}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-2}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-8x } & = & -2 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+14}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-5x } & = & -4 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-x } & = & 12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+14}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-8x } & = & -1 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-14}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+13x } & = & 11 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &22x & = &25\\\Leftrightarrow & \color{red}{22}x & = &25\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{25}{22} \\\Leftrightarrow & \color{green}{ x = \frac{25}{22} } & & \\ & V = \left\{ \frac{25}{22} \right\} & \\\end{align}\)