Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+15}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & 7 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-8}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & -3 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-2}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-5x } & = & 8 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-6}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+13x } & = & -4 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-13}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & -3 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-25x & = &10\\\Leftrightarrow & \color{red}{-25}x & = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+8}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+2x } & = & -14 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & 1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-4}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+3x } & = & -9 \color{red}{ -3x }\color{blue}{+4+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+15}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-4x } & = & 14 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)