Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+8}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & 5 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-14}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-10x } & = & 8 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &-23x & = &22\\\Leftrightarrow & \color{red}{-23}x & = &22\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{22}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{23} } & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+10}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-9x } & = & -10 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-2x & = &-20\\\Leftrightarrow & \color{red}{-2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-20}{-2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-7}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-13x } & = & -10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &-28x & = &-3\\\Leftrightarrow & \color{red}{-28}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{28} } & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-10}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+11x } & = & -10 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-x } & = & 2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+5}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x } & = & 8 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-11}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11+7x } & = & -14 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)