Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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