Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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