Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-3}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-13x } & = & -4 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-x } & = & 5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-3}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-7x } & = & -10 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &9x & = &23\\\Leftrightarrow & \color{red}{9}x & = &23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-7}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & 13 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &23x & = &20\\\Leftrightarrow & \color{red}{23}x & = &20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & 14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+10}& = & -4 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+4x } & = & -4 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-14}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+13x } & = & -14 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &22x & = &0\\\Leftrightarrow & \color{red}{22}x & = &0\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{0}{22} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+15}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-9x } & = & -5 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &2x & = &18\\\Leftrightarrow & \color{red}{2}x & = &18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{18}{2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-9}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-9x } & = & 1 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)