Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+13}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & 3 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &15x & = &-10\\\Leftrightarrow & \color{red}{15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-4}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x } & = & 8 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &27x & = &12\\\Leftrightarrow & \color{red}{27}x & = &12\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{12}{27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+15}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+14x } & = & 10 \color{red}{ -14x }\color{blue}{-15+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &29x & = &-5\\\Leftrightarrow & \color{red}{29}x & = &-5\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-5}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{29} } & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+10}& = & 1 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10-12x } & = & 1 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-5x } & = & -8 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-12}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-7x } & = & 9 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &x & = &21\\\Leftrightarrow & \color{red}{}x & = &21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 21 \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & -14 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &27x & = &-6\\\Leftrightarrow & \color{red}{27}x & = &-6\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-6}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & 11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)