Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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