Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-15}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-13x } & = & -11 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-28x & = &4\\\Leftrightarrow & \color{red}{-28}x & = &4\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{4}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-14}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-11x } & = & -3 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x } & = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-13}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+13x } & = & 8 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &22x & = &21\\\Leftrightarrow & \color{red}{22}x & = &21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{21}{22} } & & \\ & V = \left\{ \frac{21}{22} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-4}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-7x } & = & -15 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-11}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11+11x } & = & -15 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-10}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-13x } & = & 11 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-4x & = &21\\\Leftrightarrow & \color{red}{-4}x & = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-15}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-13x } & = & -6 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-2}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+4x } & = & 1 \color{red}{ -4x }\color{blue}{+2+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)