Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+3}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-13x } & = & -5 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &2x & = &-8\\\Leftrightarrow & \color{red}{2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-8}{2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-10}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+6x } & = & 6 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-10}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+5x } & = & 1 \color{red}{ -5x }\color{blue}{+10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+4}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-6x } & = & 15 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+13}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-11x } & = & -8 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-10}& = & 11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+4x } & = & 11 \color{red}{ -4x }\color{blue}{+10+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &9x & = &21\\\Leftrightarrow & \color{red}{9}x & = &21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-26\\\Leftrightarrow & \color{red}{-8}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-9}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-11x } & = & -1 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-5}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-7x } & = & -5 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+9}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-12x } & = & -9 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-18\\\Leftrightarrow & \color{red}{-23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-10}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-3x } & = & -13 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-14}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-9x } & = & -2 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)