Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-14}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14+2x } & = & -15 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+13}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-2x } & = & -12 \color{red}{ +2x }\color{blue}{-13-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &x & = &-25\\\Leftrightarrow & \color{red}{}x & = &-25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -25 \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+11}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-11x } & = & 10 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+3}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+5x } & = & 3 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+2}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+9x } & = & -6 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &13x & = &24\\\Leftrightarrow & \color{red}{13}x & = &24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+11}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+3x } & = & -12 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-10}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-8x } & = & 11 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+7}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-11x } & = & -6 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-13}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-11x } & = & -7 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+9}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-7x } & = & -9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)