Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+5}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-5x } & = & -11 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-5}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-7x } & = & 10 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-20x & = &15\\\Leftrightarrow & \color{red}{-20}x & = &15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-16x & = &10\\\Leftrightarrow & \color{red}{-16}x & = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-5}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+13x } & = & 14 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &27x & = &19\\\Leftrightarrow & \color{red}{27}x & = &19\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{19}{27} \\\Leftrightarrow & \color{green}{ x = \frac{19}{27} } & & \\ & V = \left\{ \frac{19}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+10}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-3x } & = & -11 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-21\\\Leftrightarrow & \color{red}{-14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-11}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-13x } & = & 10 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-2x & = &21\\\Leftrightarrow & \color{red}{-2}x & = &21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = & 10 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+10x } & = & 10 \color{red}{ -10x }\color{blue}{-1+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+14}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-5x } & = & 2 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)