Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+8}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-4x } & = & 4 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-8}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-11x } & = & -14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-2}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-13x } & = & -5 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & 11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+2x } & = & 1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-5}& = & -10 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+10x } & = & -10 \color{red}{ -10x }\color{blue}{+5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+11}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-14x } & = & -8 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &3x & = &-3\\\Leftrightarrow & \color{red}{3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-3}{3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)