Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+11}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+14x } & = & -5 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &29x & = &-16\\\Leftrightarrow & \color{red}{29}x & = &-16\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-16}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{29} } & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-11}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-11x } & = & 3 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-8}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+6x } & = & 14 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &19x & = &22\\\Leftrightarrow & \color{red}{19}x & = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+10}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-5x } & = & 15 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-15}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+11x } & = & -6 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &20x & = &9\\\Leftrightarrow & \color{red}{20}x & = &9\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{9}{20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-5}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+11x } & = & 6 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &26x & = &11\\\Leftrightarrow & \color{red}{26}x & = &11\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{11}{26} \\\Leftrightarrow & \color{green}{ x = \frac{11}{26} } & & \\ & V = \left\{ \frac{11}{26} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-6}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-13x } & = & -3 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x } & = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-11\\\Leftrightarrow & \color{red}{-17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+1}& = & 14 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+12x } & = & 14 \color{red}{ -12x }\color{blue}{-1+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &11x & = &13\\\Leftrightarrow & \color{red}{11}x & = &13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-2}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-5x } & = & 11 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)