Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-8x+1=-15+9x\)
2. \(-x-4=-3+0x\)
3. \(-13x+10=-6+x\)
4. \(2x+15=-10+x\)
5. \(-x+13=14+11x\)
6. \(-3x+5=2+7x\)
7. \(-5x-3=7+x\)
8. \(13x+8=7+3x\)
9. \(-13x+15=-1+x\)
10. \(-10x+8=-9+11x\)
11. \(9x+9=-8+2x\)
12. \(3x+11=13-14x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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