Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+7}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-9x } & = & -15 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+15}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-9x } & = & -8 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &5x & = &-23\\\Leftrightarrow & \color{red}{5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-23}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-6}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-13x } & = & -14 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-28x & = &-8\\\Leftrightarrow & \color{red}{-28}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-8}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+11}& = & -13 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-6x } & = & -13 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-7}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-11x } & = & -6 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+9}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & -1 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+5}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+2x } & = & -3 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-10}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-8x } & = & 13 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &3x & = &23\\\Leftrightarrow & \color{red}{3}x & = &23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-13}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-3x } & = & 10 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+7}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-14x } & = & -7 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+3}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-5x } & = & 2 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)