Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+11}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-8x } & = & -3 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-14\\\Leftrightarrow & \color{red}{-23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{14}{23} } & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & 15 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-12x & = &28\\\Leftrightarrow & \color{red}{-12}x & = &28\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{28}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & 8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+13}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-8x } & = & 15 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-21x & = &2\\\Leftrightarrow & \color{red}{-21}x & = &2\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{2}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{21} } & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+1}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-8x } & = & -2 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-10}& = & -3 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-6x } & = & -3 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+9}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-3x } & = & -8 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+15}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-10x } & = & 7 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+11}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-13x } & = & 12 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)