Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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