Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+13}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-7x } & = & -2 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+12}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-13x } & = & -8 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-20\\\Leftrightarrow & \color{red}{-19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-20}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-11}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-3x } & = & 5 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-2}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+11x } & = & -6 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &26x & = &-4\\\Leftrightarrow & \color{red}{26}x & = &-4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-3}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-3x } & = & 5 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+9}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-8x } & = & 12 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-12}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-9x } & = & -8 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+1}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-12x } & = & 10 \color{red}{ +12x }\color{blue}{-1-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-23x & = &9\\\Leftrightarrow & \color{red}{-23}x & = &9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-9}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+11x } & = & 7 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)