Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+13}& = & -7 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-15x } & = & -7 \color{red}{ +15x }\color{blue}{-13-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-15}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15+7x } & = & 2 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+10}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-13x } & = & -13 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-23\\\Leftrightarrow & \color{red}{-17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{23}{17} } & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-11}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+8x } & = & 1 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-3}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-8x } & = & 2 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+5}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-11x } & = & 12 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-18x & = &7\\\Leftrightarrow & \color{red}{-18}x & = &7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{18} } & & \\ & V = \left\{ \frac{-7}{18} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+11}& = & -8 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11-6x } & = & -8 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+12}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-13x } & = & -3 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &-25x & = &-15\\\Leftrightarrow & \color{red}{-25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-2}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-11x } & = & -3 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+10}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-5x } & = & -10 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)