Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+11}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+7x } & = & 12 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-10}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-8x } & = & -8 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+9}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-7x } & = & -15 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-24\\\Leftrightarrow & \color{red}{-16}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+8}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8+7x } & = & -10 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-2}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+4x } & = & -9 \color{red}{ -4x }\color{blue}{+2+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+12}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-3x } & = & 2 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+1}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-13x } & = & 11 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+7}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)