Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+7}& = & 1 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-12x } & = & 1 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & -11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-14}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+2x } & = & 4 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-7}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+8x } & = & -9 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+13}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-11x } & = & 1 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-11}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-11x } & = & -14 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-6}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-3x } & = & -12 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+6}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+10x } & = & 4 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &21x & = &-2\\\Leftrightarrow & \color{red}{21}x & = &-2\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-2}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{21} } & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+2}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-5x } & = & -4 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)