Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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