Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+5}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-9x } & = & -15 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-10x & = &-20\\\Leftrightarrow & \color{red}{-10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-20}{-10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+1}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+2x } & = & 8 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-15}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-3x } & = & 1 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+9}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+5x } & = & -5 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+4}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-11x } & = & -10 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-21x & = &-14\\\Leftrightarrow & \color{red}{-21}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-14}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-2}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-7x } & = & 2 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-8}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-5x } & = & -15 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-24\\\Leftrightarrow & \color{red}{-7}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-10x & = &23\\\Leftrightarrow & \color{red}{-10}x & = &23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{10} } & & \\ & V = \left\{ \frac{-23}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-14}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+6x } & = & -9 \color{red}{ -6x }\color{blue}{+14+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+4x } & = & -12 \color{red}{ -4x }\color{blue}{-15+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &17x & = &-27\\\Leftrightarrow & \color{red}{17}x & = &-27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{17} } & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)