Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-1}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+11x } & = & 11 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &25x & = &12\\\Leftrightarrow & \color{red}{25}x & = &12\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{12}{25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+14}& = & 14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+15x } & = & 14 \color{red}{ -15x }\color{blue}{-14+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+11}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-14x } & = & 8 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-1}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-7x } & = & 3 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+8}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+8x } & = & 7 \color{red}{ -8x }\color{blue}{-8+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & 1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-14}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-9x } & = & -12 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+1}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-7x } & = & -9 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)