Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-7}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & -7 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-13x } & = & -11 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-28x & = &-5\\\Leftrightarrow & \color{red}{-28}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{28} } & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+8}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-12x } & = & -3 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+8}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-6x } & = & -1 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+15}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15-11x } & = & 12 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-5}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-3x } & = & 4 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+11x } & = & 13 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &26x & = &15\\\Leftrightarrow & \color{red}{26}x & = &15\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{15}{26} \\\Leftrightarrow & \color{green}{ x = \frac{15}{26} } & & \\ & V = \left\{ \frac{15}{26} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+8}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+9x } & = & -13 \color{red}{ -9x }\color{blue}{-8+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)