Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+7}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-12x } & = & 4 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-9x } & = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-22x & = &-11\\\Leftrightarrow & \color{red}{-22}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-11}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-3}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+8x } & = & 5 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+3}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-5x } & = & 14 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-4}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+7x } & = & -8 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-2}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+11x } & = & 9 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+9}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+7x } & = & -10 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-11}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+12x } & = & 15 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &25x & = &26\\\Leftrightarrow & \color{red}{25}x & = &26\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{26}{25} \\\Leftrightarrow & \color{green}{ x = \frac{26}{25} } & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)